Chapter 2 Review Homework
You are applying for a job at two companies. Company A offers starting salaries with *μ* = $35,000 and *σ* = $2,000. Company B offers starting salaries with *μ* = $35,000 and *σ* = $5,000. From which company are you more likely to get an offer of $39,000 or more? Choose the correct answer below. A.) Company A, because data values that lie more than two standard deviations from the mean are considered unusual. B.) No difference, because data values that lie more than three standard deviations from the mean are considered very unusual. C.) Company B, because data values that lie within one standard deviation from the mean are not considered unusual.
Correct Answer: C.) Company B, because data values that lie within one standard deviation from the mean are not considered unusual. (*2.4.19*)
The mean value of land and buildings per acre from a sample of farms is $1700, with a standard deviation of $100. The data set has a bell-shaped distribution. Assume the number of farms in the sample is 76. *Part 1 (a):* Use the empirical rule to estimate the number of farms whose land and building values per acre are between $1500 and $1900. (Round answer to the *nearest whole number* (*zero* decimal places).) *__* farms *Part 2 (b):* If 25 additional farms were sampled, about how many of these additional farms would you expect to have land and building values between $1500 per acre and $1900 per acre? (Round answer to the *nearest whole number* (*zero* decimal places).) *__* farms out of 25
Correct Answers: *Part 1 (a):* *72* *Part 2 (b):* *24* (*2.4.31*)
Use the box-and-whisker plot to identify the five-number summary. (Since I don't have Quizlet+, I can't insert the actual image of the box-and-whisker plot; ergo, I pasted the description.) A box-and-whisker plot has a *horizontal axis* labeled from *10 to 22* in *increments of "1"*. Vertical line segments are drawn at the following values: *13*, *15*, and *16*. A box encloses the *vertical line segments* at *13*, *15*, and *16*, and *horizontal line segments* extend outward from both sides of the box to points plotted at *10* and *21*. All values are approximate. *Part 1:* Min = *__* *Part 2:* Q₁ = *__* *Part 3:* Q₂ = *__* *Part 4:* Q₃ = *__* *Part 5:* Max = *__*
Correct Answers: *Part 1:* *10* *Part 2:* *13* *Part 3:* *15* *Part 4:* *16* *Part 5:* *21* (*2.5.13*)
Use the frequency distribution shown below to construct an expanded frequency distribution. *High Temperatures (°F)* *Class* *(1):* 15-25 *(2):* 26-36 *(3):* 37-47 *(4):* 48-58 *(5):* 59-69 *(6):* 70-80 *(7):* 81-91 *Frequency, ƒ* *(1):* 17 *(2):* 45 *(3):* 66 *(4):* 67 *(5):* 82 *(6):* 66 *(7):* 22 Complete the table below. (Round answers to the *nearest hundredth* (*two* decimal places).) *High Temperatures (°F)* Class (I) Frequency, ƒ (II) *Midpoint (III)* *Relative frequency (IV)* *Cumulative frequency (V)* *(1):* *I:* 15-25 *II:* 17 *III:* *__* *IV:* *___* *V:* *__* *(2):* *I:* 26-36 *II:* 45 *III:* *__* *IV:* *___* *V:* *__* *(3):* *I:* 37-47 *II:* 66 *III:* *__* *IV:* *___* *V:* *___* *(4):* *I:* 48-58 *II:* 67 *III:* *__* *IV:* *___* *V:* *___* *(5):* *I:* 59-69 *II:* 82 *III:* *__* *IV:* *___* *V:* *___* *(6):* *I:* 70-80 *II:* 66 *III:* *__* *IV:* *___* *V:* *___* *(7):* *I:* 81-91 *II:* 22 *III:* *__* *IV:* *___* *V:* *___*
Correct Answers (*Midpoint*; *"Relative" Frequency*; *"Cumulative" Frequency*): *(1):* *20*; *0.05*; *17* *(2):* *31*; *0.12*; *62* *(3):* *42*; *0.18*; *128* *(4):* *53*; *0.18*; *195* *(5):* *64*; *0.22*; *277* *(6):* *75*; *0.18*; *343* *(7):* *86*; *0.06*; *365* (*2.1.18*)
Use the given minimum and maximum data entries, and the number of classes, to find the class width, the lower class limits, and the upper class limits. *minimum = 9, maximum = 65, 6 classes* *Part 1:* The class width is *__*. *Part 2:* Choose the correct lower class limits below. A.) 18, 28, 39, 48, 58, 68 B.) 9, 18, 29, 38, 48, 59 C.) 19, 28, 39, 49, 59, 68 D.) 9, 19, 29, 39, 49, 59 *Part 3:* Choose the correct upper class limits below. A.) 18, 28, 39, 49, 58, 68 B.) 19, 29, 39, 49, 59, 68 C.) 19, 29, 38, 48, 59, 68 D.) 18, 28, 38, 48, 58, 68
Correct Answers: *Part 1:* *10* *Part 2:* D.) 9, 19, 29, 39, 49, 59 *Part 3:* D.) 18, 28, 38, 48, 58, 68 (*2.1.12*)
Construct the described data set. The entries in the data set cannot all be the same. *The mean is "not" representative of a typical number in the data set.* *Part 1:* What is the definition of mean? A.) The data entry that occurs with the greatest frequency. B.) The value that lies in the middle of the data when the data set is ordered. C.) The sum of the data entries divided by the number of entries. D.) The data entry that is far removed from the other entries in the data set. *Part 2:* Choose the data set whose mean is not equal to a value in the set. A.) 2, 2, 2, 3, 4, 4, 4 B.) 1, 3, 5, 7, 9 C.) 16, 17, 18, 19, 20 D.) 1, 1, 3, 3
Correct Answers: *Part 1:* C.) The sum of the data entries divided by the number of entries. *Part 2:* D.) 1, 1, 3, 3 (*2.3.7*)
Determine whether the statement is true or false. If it is false, rewrite it as a true statement. *Some quantitative data sets do not have medians.* Choose the correct answer below. A.) The statement is true. B.) The statement is false. All quantitative data set have medians. C.) The statement is false. Some quantitative data sets have more than one median. D.) The statement is false. Some quantitative data sets do not have means.
Correct Answer: B.) The statement is false. All quantitative data set have medians. (*2.3.2*)
Determine whether the following statement is true or false. If it is false, rewrite it as a true statement. *The mean is the measure of central tendency most likely to be affected by an outlier.* Choose the correct answer below. A.) The statement is false. The mode is the measure of central tendency most likely to be affected by an outlier. B.) The statement is false. Outliers do not affect any measure of central tendency. C.) The statement is false. The median is the measure of central tendency most likely to be affected by an outlier. D.) The statement is true.
Correct Answer: D.) The statement is true. (*2.3.1*)
*(A (parts 1-5))* Find the five-number summary, and *(B (part 6))* draw a box-and-whisker plot of the data. *2 8 8 5 1 9 8 7 9 5 9 4 1 6 1 9 8 7 7 9* *Part 1 (a):* Min = *_* (*Simplify* the answer.) *Part 2 (a):* Q₁ = *__* (*Simplify* the answer, but *DO NOT ROUND*.) *Part 3 (a):* Q₂ = *_* (*Simplify* the answer, but *DO NOT ROUND*.) *Part 4 (a):* Q₃ = *__* (*Simplify* the answer, but *DO NOT ROUND*.) *Part 5 (a):* Max = *_* (*Simplify* the answer.) *Part 6 (b):* Choose the correct box-and-whisker plot below. (Since I don't have Quizlet+, I can't insert the actual images of the box-and-whisker plots; ergo, I pasted their descriptions.) A.) A box-and-whisker plot has a *horizontal axis* labeled from *1 to 9* in *increments of "1"*. Vertical line segments are drawn at the following values: *4.5*, *7*, and *8.5*. A box encloses the *"vertical" line segments* at *4.5*, *7*, and *8.5*, and *"horizontal" line segments* extend outward from both sides of the box to points at *1* and *9*. All values are approximate. B.) A box-and-whisker plot has a *horizontal axis* labeled from *1 to 9* in *increments of "1"*. Vertical line segments are drawn at the following values: *4.5*, *7*, and *8.5*. A box encloses the *"vertical" line segments* at *4.5*, *7*, and *8.5*, and a *"horizontal" line segment* extends outward from *the right side of the box* to *the point at "9"*. All values are approximate. C.) A box-and-whisker plot has a *horizontal axis* labeled from *1 to 9* in *increments of "1"*. Vertical line segments are drawn at the following values: *4*, *6.5*, and *8*. A box encloses the *"vertical" line segments* at *4*, *6.5*, and *8*, and *"horizontal" line segments* extend outward from both sides of the box to points at *1* and *9*. All values are approximate. D.) A box-and-whisker plot has a *horizontal axis* labeled from *1 to 9* in *increments of "1"*. Vertical line segments are drawn at the following values: *4.5*, *8.5*, and *9*. A box encloses the *"vertical" line segments* at *4.5*, *8.5*, and *9*, and a *"horizontal" line segment* extends outward from *the left side of the box* to *the point at "1"*. All values are approximate.
Correct Answers: *Part 1 (a):* *1* *Part 2 (a):* *4.5* *Part 3 (a):* *7* *Part 4 (a):* *8.5* *Part 5 (a):* *9* *Part 6 (b):* A.) A box-and-whisker plot has a *horizontal axis* labeled from *1 to 9* in *increments of "1"*. Vertical line segments are drawn at the following values: *4.5*, *7*, and *8.5*. A box encloses the *"vertical" line segments* at *4.5*, *7*, and *8.5*, and *"horizontal" line segments* extend outward from both sides of the box to points at *1* and *9*. All values are approximate. (*2.5.17*)
Use the Empirical Rule. The mean speed of a sample of vehicles along a stretch of highway is 70 miles per hour, with a standard deviation of 3 miles per hour. Estimate the percent of vehicles whose speeds are between 61 miles per hour and 79 miles per hour. (Assume the data set has a bell-shaped distribution.) Approximately *___%* of vehicles travel between 61 miles per hour and 79 miles per hour.
Correct Answer: *99.7%* (*2.4.29*)
Use the box-and-whisker plot to identify the five-number summary. (Since I don't have Quizlet+, I can't insert the actual image of the box-and-whisker plot; ergo, I pasted the description.) A box-and-whisker plot has a *horizontal axis* labeled from *900 to 2100* in *increments of "300"*. Points are drawn at the following values: *886*, *1204*, *1468*, *1901*, and *2074*, and vertical line segments are drawn at *1204*, *1468*, and *1901*. A box encloses the *"vertical" line segments* at *1204*, *1468*, and *1901*, and *"horizontal" line segments* connect all plotted points. All points are labeled with their values. *Part 1:* Min = *___* *Part 2:* Q₁ = *____* *Part 3:* Q₂ = *____* *Part 4:* Q₃ = *____* *Part 5:* Max = *____*
Correct Answers: *Part 1:* *886* *Part 2:* *1204* *Part 3:* *1468* *Part 4:* *1901* *Part 5:* *2074* (*2.5.14*)
Why is the standard deviation used more frequently than the variance? Choose the correct answer below. A.) The standard deviation is easier to compute. B.) The units of variance are squared. Its units are meaningless. C.) The standard deviation requires less entries from the data set.
Correct Answer: B.) The units of variance are squared. Its units are meaningless. (*2.4.3*)
A motorcycle's fuel efficiency represents the ninth decile of vehicles in its class. Make an observation about the motorcycle's fuel efficiency. Choose the correct answer below. A.) The motorcycle's fuel efficiency is greater than the fuel efficiency for 100% of vehicles in its class. B.) The motorcycle's fuel efficiency is greater than the fuel efficiency for 10% of vehicles in its class. C.) The motorcycle's fuel efficiency is greater than the fuel efficiency for 9% of vehicles in its class. D.) The motorcycle's fuel efficiency is greater than the fuel efficiency for 90% of vehicles in its class.
Correct Answer: D.) The motorcycle's fuel efficiency is greater than the fuel efficiency for 90% of vehicles in its class. (*2.5.2*)
Find the range of the data set represented by the graph. (Since I don't have Quizlet+, I can't insert the actual image of the bar graph; ergo, I pasted the description.) A bar graph titled *"Woman's Age at First Childbirth"* has a *horizontal axis* labeled *"Age (in years)"* from *24 to 34* in *increments of "1" year*, and a *vertical axis* labeled *"Frequency"* from *0 to 10* in *increments of "1"*. There are vertical bars, each of which is over a horizontal axis label. The heights of the bars are as follows, where the *horizontal axis label* is listed *first*, and the *height* is listed *second*: *(24, 2); (25, 5); (26, 4); (27, 4); (28, 8); (29, 10); (30, 7); (31, 5); (32, 4); (33, 5); (34, 3)*. The range of the data set is *__*.
Correct Answer: *10* (*2.4.9*)
Find the range of the data set represented by the graph (*simplify* the answer). (Since I don't have Quizlet+, I can't insert the actual image of the dot plot; ergo, I pasted the description.) A dot plot has a *horizontal axis* labeled from *70 to 100* in *increments of "1"*. The graph consists of a series of plotted points from left to right. The coordinates of the plotted points are as follows, where the *label* is listed *first*, and the *number of dots* is listed *second*: *(74, 1); (78, 2); (79, 1); (80, 4); (84, 1); (86, 2); (88, 4); (90, 2); (91, 2); (94, 1); (95, 1); (96, 1); (97, 1); (100, 1)*. The range of the data set is *__*.
Correct Answer: *26* (*2.4.10*)
Use the frequency polygon to identify the class with the greatest, and the class with the least, frequency. (Since I don't have Quizlet+, I can't insert the actual image of the frequency polygon; ergo, I pasted the description.) A frequency polygon titled *"Raw MCAT Scores"* has a *horizontal axis* labeled *Score* from *4 to 43 in *increments of "1.5"*, and a *vertical axis* labeled *Frequency* from *0 to 16* in *increments of "2"*. Plotted points are connected by line segments from left to right. The heights of the plotted points are as follows, where the *score* is listed *first*, and the *frequency* is listed *second*: *(7, 0); (10, 1); (13, 2); (16, 3); (19, 6); (22, 7); (25, 12); (28, 14); (31, 10); (34, 6); (37, 2); (40, 0)*. *Part 1:* What are the boundaries of the class with the greatest frequency? A.) 25.5-30.5 B.) 25-31 C.) 28-31 D.) 26.5-29.5 *Part 2:* What are the boundaries of the class with the least frequency? A.) 7-13 B.) 7.5-12.5 C.) 8.5-11.5 D.) 10-13
Correct Answer: *Part 1:* D.) 26.5-29.5 *Part 2:* C.) 8.5-11.5 (*2.1.21*)
Both data sets have a mean of 145. One has a standard deviation of 16, and the other has a standard deviation of 24. Key: *10* | *8* = *108* *(a):* *10* | *8* *9* *11* | *1 *5* *8* *12 | *1* *1* *13* | *0* *0* *6* *7* *14* | *1* *5* *9* *15* | *1* *3* *6* *8* *16* | *0* *9* *9* *17* | *9* *18* | *3* *5* *7* *(b):* *10* | *11* | *1* *12* | *2* *3* *5* *13* | *0* *3* *5* *7* *8* *14* | *1* *1* *2* *3* *3* *3* *15* | *1* *5* *8* *8* *16* | *2* *3* *4* *5* *17* | *0* *9* *18* | Which data set has which deviation? A.) *(a)* has a standard deviation of 24 and *(b)* has a standard deviation of 16, because the data in *(a)* have more variability. B.) *(a)* has a standard deviation of 16 and *(b)* has a standard deviation of 24, because the data in *(b)* have less variability.
Correct Answer: A.) *(a)* has a standard deviation of 24 and *(b)* has a standard deviation of 16, because the data in *(a)* have more variability. (*2.4.18*)
The goals scored per game by a soccer team represent the first quartile for all teams in a league. What can you conclude about the team's goals scored per game? Choose the correct answer below. A.) The team scored fewer goals per game than 25% of the teams in the league. B.) The team scored fewer goals per game than 75% of the teams in the league. C.) The team scored fewer goals per game than 100% of the teams in the league. D.) The team scored fewer goals per game than 50% of the teams in the league.
Correct Answer: B.) The team scored fewer goals per game than 75% of the teams in the league. (*2.5.1*)
Why should the number of classes in a frequency distribution be between 5 and 20? Choose the correct answer below. A.) The number of classes in a frequency distribution should be between 5 and 20 so that the class width is between 5 and 20. B.) The number of classes in a frequency distribution should be between 5 and 20 so that the class width is not too large. C.) If the number of classes in a frequency distribution is not between 5 and 20, it may be difficult to detect any patterns. D.) The number of classes in a frequency distribution should be between 5 and 20 so that the classes do not overlap. E.) The number of classes in a frequency distribution should be between 5 and 20 so that the class width is not too small.
Correct Answer: C.) If the number of classes in a frequency distribution is not between 5 and 20, it may be difficult to detect any patterns. (*2.1.2*)
Without performing any calculations, determine which measure of central tendency best represents the graphed data. (Since I don't have Quizlet+, I can't insert the actual image of the bar graph; ergo, I pasted the description.) A bar graph titled *"How Often Do You Change Jobs?"* has a *vertical axis* labeled *"Frequency"* from *0 to 1250* in *increments of "250"*. There are vertical bars with labels and heights as follows: *(Every 1-3 years, 431); (Every 4-5 years, 329); (Every 6-10 years, 1140); (Stayed at one job longer than 10 years, 587)*. Choose the correct answer below. A.) The mean is the best representation of the data. The distribution is uniform and there are no outliers. B.) The mean is the best representation of the data. The distribution is symmetric and there are no outliers. C.) The mode is the best representation of the data. The data are at the nominal level of measurement. D.) The median is the best representation of the data. The distribution is skewed left with several outliers. E.) The mode is the best representation of the data. The distribution is uniform and there are no outliers. F.) The median is the best representation of the data. The distribution is skewed right with several outliers.
Correct Answer: C.) The mode is the best representation of the data. The data are at the nominal level of measurement. (*2.3.37*)
Determine whether the approximate shape of the distribution in the histogram shown is symmetric, uniform, skewed left, skewed right, or none of these. Justify your answer. (Since I don't have Quizlet+, I can't insert the actual image of the histogram; ergo, I pasted the description.) A histogram has a *horizontal axis* labeled from *15000 to 105000* in *increments of "10000"*, and a *vertical axis* labeled from *0 to 20* in *increments of "2"*. The histogram has vertical bars of width 10000, where each vertical bar is centered over a horizontal axis tick mark. The heights of the vertical bars are as follows, where the *horizontal center of the bar* is listed *first*, and the *height* is listed *second*: *(25000, 19); (35000, 14); (45000, 8); (55000, 5); (65000, 3); (75000, 4); (85000, 3); (95000, 1)*. Choose the correct answer below. A.) The shape of the distribution is skewed left because the bars have a tail to the left. B.) The shape of the distribution is symmetric, but not uniform, because a vertical line can be drawn down the middle, creating two halves that look approximately the same. C.) The shape of the distribution is skewed right because the bars have a tail to the right. D.) The shape of the distribution is uniform because the bars are approximately the same height. E.) The shape of the distribution is none of these because the bars do not show any of these general trends.
Correct Answer: C.) The shape of the distribution is skewed right because the bars have a tail to the right. (*2.3.9*)
Determine whether the approximate shape of the distribution in the histogram shown is symmetric, uniform, skewed left, skewed right, or none of these. Justify your answer. (Since I don't have Quizlet+, I can't insert the actual image of the histogram; ergo, I pasted the description.) A histogram has a *horizontal axis* labeled from *75 to 165* in *increments of "10"*, and a *vertical axis* labeled from *0 to 18* in *increments of "3"*. The histogram has vertical bars of width 10, where each vertical bar is centered over a horizontal axis tick mark. The heights of the vertical bars are as follows, where the *horizontal center of the bar* is listed *first*, and the *height* is listed *second*: *(85, 2); (95, 6); (105, 11); (115, 14); (125, 15); (135, 11); (145, 5); (155, 4)*. Choose the correct answer below. A.) The shape of the distribution is skewed right because the bars have a tail to the right. B.) The shape of the distribution is skewed left because the bars have a tail to the left. C.) The shape of the distribution is symmetric, but not uniform, because a vertical line can be drawn down the middle, creating two halves that look approximately the same. D.) The shape of the distribution is uniform because the bars are approximately the same height. E.) The shape of the distribution is none of these because the bars do not show any of these general trends.
Correct Answer: C.) The shape of the distribution is symmetric, but not uniform, because a vertical line can be drawn down the middle, creating two halves that look approximately the same. (*2.3.10*)
Without performing any calculations, determine which measure of central tendency best represents the graphed data. (Since I don't have Quizlet+, I can't insert the image of the actual histogram; ergo, I pasted the description.) Explain your reasoning. A histogram titled *"Heart Rates of a Sample of Adults"* has a *horizontal axis* labeled *Heart Rate (beats per minute)* from *55 to 85* in *increments of "5"*, and a *vertical axis* labeled *Frequency* from *0 to 50* in *increments of "5"*. The histogram contains vertical bars of width 5, where one vertical bar is centered over each of the horizontal axis tick marks. The heights of the vertical bars are listed as follows, where the *label* is listed *first*, and the *height* is listed *second*: *(55, 4); (60, 7); (65, 13); (70, 20); (75, 25); (80, 32); (85, 43)*. Choose the correct answer below. A.) The mode is the best measure because the data are at the nominal level of measurement. B.) The mean is the best measure because there are outliers and the data is skewed. C.) The mean is the best measure because the data are approximately symmetric. D.) The median is the best measure because the data.
Correct Answer: D.) The median is the best measure because the data. (*2.3.39*)
Use the accompanying data set to complete the following actions. *Part 1 (a):* Find the quartiles. (Type answers as either *integers* or *decimals*.) *Part 2 (b):* Find the interquartile range. (Type answer as either an *integer* or a *decimal*.) *Part 3 (c):* Identify any outliers. (Use a *comma* to separate answers (if needed).) *42 52 35 43 40 36 41 47 45 37 34 56 43 35 15 51 39 51 30 30* *Part 1 (a):* Find the quartiles. The first quartile, Q₁, is *_(1)_*. The second quartile, Q₂, is *__(2)__*. The third quartile, Q₃, is *_(3)_*. *Part 2 (b):* Find the interquartile range. The interquartile range (IQR) is *__*. *Part 3 (c):* Identify any outliers. Choose the correct answer below. A.) There exists at least one outlier in the data set at *__*. B.) There are no outliers in the data set.
Correct Answers: *Part 1 (a):* *(1):* *35* *(2):* *40.5* *(3):* *46* *Part 2 (b):* *11* *Part 3 (c):* A.) There exists at least one outlier in the data set at *15*. (*2.5.12*)
Use the accompanying data set to complete the following actions. *Part 1 (a):* Find the quartiles. (Type answers as either *integers* or *decimals*.) *Part 2 (b):* Find the interquartile range. (Type answer as either an *integer* or a *decimal*.) *Part 3 (c):* Identify any outliers. (Use a *comma* to separate answers (if needed).) *57 64 54 57 64 55 59 61 64 61 62 57 60 65 78* *Part 1 (a):* Find the quartiles. The first quartile, Q₁, is *_(1)_*. The second quartile, Q₂, is *_(2)_*. The third quartile, Q₃, is *_(3)_*. *Part 2 (b):* Find the interquartile range. The interquartile range (IQR) is *_*. *Part 3 (c):* Identify any outliers. Choose the correct answer below. A.) There exists at least one outlier in the data set at *__*. B.) There are no outliers in the data set.
Correct Answers: *Part 1 (a):* *(1):* *57* *(2):* *61* *(3):* *64* *Part 2 (b):* *7* *Part 3 (c):* A.) There exists at least one outlier in the data set at *78*. (*2.5.11*)
Use the given minimum and maximum data entries, and the number of classes, to find *(a)* the class width (type answer as a *whole number* (*zero* decimal places)), *(b)* the lower class limits, and *(b)* the upper class limits (type answers as *whole numbers* (*zero* decimal places), and use a *comma* to separate answers (if needed)). *minimum = 10, maximum = 97, 7 classes* *Part 1 (a):* The class width is *__*. *(b):* Use the minimum as the first lower class limit, and then find the remaining lower class limits. *Part 2 (b):* The lower class limits are *__, __, __, __, __, __, __*. *Part 3 (b):* The upper class limits are *__, __, __, __, __, __, ___*.
Correct Answers: *Part 1 (a):* *13* *Part 2 (b):* *10, 23, 36, 49, 62, 75, 88* *Part 3 (b):* *22, 35, 48, 61, 74, 87, 100* (*2.1.11*)
*(A (parts 1-5))* Find the five-number summary, and *(B (part 6))* draw a box-and-whisker plot of the data. *4 8 8 6 2 9 8 7 9 6 9 5 2 6 2 9 8 7 7 9* *Part 1 (a):* Min = *_* (*Simplify* the answer.) *Part 2 (a):* Q₁ = *__* (*Simplify* the answer, but *DO NOT ROUND*.) *Part 3 (a):* Q₂ = *_* (*Simplify* the answer, but *DO NOT ROUND*.) *Part 4 (a):* Q₃ = *__* (*Simplify* the answer, but *DO NOT ROUND*.) *Part 5 (a):* Max = *_* (*Simplify* the answer.) *Part 6 (b):* Choose the correct box-and-whisker plot below. (Since I don't have Quizlet+, I can't insert the actual images of the box-and-whisker plots; ergo, I pasted their descriptions.) A.) A box-and-whisker plot has a *horizontal axis* labeled from *3 to 9* in *increments of "1"*. Vertical line segments are drawn at the following plotted points: *5*, *7*, and *8*. A box encloses the *"vertical" line segments* at *5*, *7*, and *8*, and *"horizontal" line segments* extend outward from both sides of the box to points plotted at *3* and *9*. All values are approximate. B.) A box-and-whisker plot has a *horizontal axis* labeled from *4 to 9* in *increments of "1"*. Vertical line segments are drawn at the following plotted points: *5*, *7*, and *9*. A box encloses the *"vertical" line segments* at *5*, *7*, and *9*, and *"horizontal" line segments* extend outward from both sides of the box to points plotted at *4* and *9*. All values are approximate. C.) A box-and-whisker plot has a *horizontal axis* labeled from *2 to 9* in *increments of "1"*. Vertical line segments are drawn at the following plotted points: *5.5*, *7*, and *8.5*. A box encloses the *"vertical" line segments* at *5.5*, *7*, and *8.5*, and *"horizontal" line segments* extend outward from both sides of the box to points plotted at *2* and *9*. All values are approximate. D.) A box-and-whisker plot has a *horizontal axis* labeled from *3 to 9* in *increments of "1"*. Vertical line segments are drawn at the following plotted points: *5*, *7*, and *8*. A box encloses the *"vertical" line segments* at *5*, *7*, and *8*, and *"horizontal" line segments* extend outward from both sides of the box to points plotted at *3* and *9*. All values are approximate.
Correct Answers: *Part 1 (a):* *2* *Part 2 (a):* *5.5* *Part 3 (a):* *7* *Part 4 (a):* *8.5* *Part 5 (a):* *9* *Part 6 (b):* C.) A box-and-whisker plot has a *horizontal axis* labeled from *2 to 9* in *increments of "1"*. Vertical line segments are drawn at the following plotted points: *5.5*, *7*, and *8.5*. A box encloses the *"vertical" line segments* at *5.5*, *7*, and *8.5*, and *"horizontal" line segments* extend outward from both sides of the box to points plotted at *2* and *9*. All values are approximate. (*2.5.15*)
Use the frequency histogram to complete the following parts. (Since I don't have Quizlet+, I can't insert the image of the actual histogram; ergo, I pasted the description.) A histogram titled *"Employee Salaries"* has a *horizontal axis* labeled *"Salary (in thousands of dollars)"* from *34.5 to 94.5* in *increments of "10"*, and a *vertical axis* labeled *"Frequency"* from *0 to 300* in *increments of "50"*. The histogram contains vertical bars of width 10, where one vertical bar is centered over each of the horizontal axis tick marks. The approximate heights of the vertical bars are listed as follows, where the *label* is listed *first*, and the *approximate height* is listed *second*: *(34.5, 20); (44.5, 110); (54.5, 280); (64.5, 300); (74.5, 160); (84.5, 90); (94.5, 40)*. *Part A (1):* Determine the number of classes. (Type answer as a *whole number* (*zero* decimal places).) *Part B (2 & 3):* Estimate the greatest and least frequencies. (Round answers to the *nearest whole number* (*zero* decimal places).) *Part C (4):* Determine the class width. (Type answer as either an *integer* or a *decimal*, but *DO NOT ROUND*.) *Part D (5):* Describe any patterns with the data. *Part 1 (a):* There are *_* classes. *Part 2 (b):* The least frequency is about *__*. *Part 3 (b):* The greatest frequency is about *___*. *Part 4 (c):* The class width is *__*. *Part 5 (d):* What pattern does the histogram show? A.) About half of the employees' salaries are between $70,000 and $89,000. B.) Most employees make less than $39,000 or more than $90,000. C.) Less than half of the employees make between $40,000 and $89,000. D.) About half of the employees' salaries are between $50,000 and $69,000.
Correct Answers: *Part 1 (a):* *7* *Part 2 (b):* *20* *Part 3 (b):* *300* *Part 4 (c):* *10* *Part 5 (d):* D.) About half of the employees' salaries are between $50,000 and $69,000. (*2.1.19*)
The data represent the time, in minutes, spent reading a political blog in a day. Construct a frequency distribution using 5 classes. In the table, include the midpoints, relative frequencies, and cumulative frequencies. Which class has the greatest frequency and which has the least frequency? *1 30 2 25 10 39 38 26 20 3 7 31 33 15 1 17 35 23 0 26* *Part 1:* Complete the table, starting with the lowest class limit. (*Simplify* the answers.) *Class (I)* *Frequency (II)* *Midpoint (III)* *Relative Frequency (IV)* *Cumulative Frequency (V)* A: *I*: *_* - *_* *II*: *_* *III*: *__* *IV*: *__* *V*: *_* B: *I*: *_* - *__* *II*: *_* *III*: *___* *IV*: *__* *V*: *_* C: *I*: *__* - *__* *II*: *_* *III*: *___* *IV*: *___* *V*: *__* D: *I*: *__* - *__* *II*: *_* *III*: *___* *IV*: *___* *V*: *__* E: *I*: *__* - *__* *II*: *_* *III*: *___* *IV*: *__* *V*: *__* *Part 2:* Which class has the greatest frequency? The class with the greatest frequency is from *_(1)_* to *_(2)_*. *Part 3:* Which class has the least frequency? The class with the least frequency is from *_(1)_* to *__(2)__*.
Correct Answers: *Part 1* (*I*; *II*; *III*; *IV*; *V*): A: *0*-*7*; *6*; *3.5*; *0.3*; *6* B: *8*-*15*; *2*; *11.5*; *0.1*; *8* C: *16*-*23*; *3*; *19.5*; *0.15*; *11* D: *24*-*31*; *5*; *27.5*; *0.25*; *16* E: *32*-*39*; *4*; *35.5*; *0.2*; *20* *Part 2:* *(1):* *0* *(2):* *7* *Part 3:* *(1):* *8* *(2):* *15* (*2.1.29*)
Construct a frequency distribution for the given data set using 6 classes. In the table, include the midpoints, relative frequencies, and cumulative frequencies. Which class has the greatest frequency and which has the least frequency? *Amount (in dollars) spent on books for a semester:* *124 490 135 191 379 538 314 338 168 449 342 461 265 448 199 521 103 256 30 426 106 422 399 407 444 178 403 88 401* *Part 1:* Complete the table, starting with the lowest class limit. Use the minimum data entry as the lower limit of the first class. (Type answers as either *integers* or *decimals*. Round the *"class limits"* to the *nearest whole number* (*zero* decimal places). Round everything else to the *nearest thousandth* (*three* decimal places).) *Class (I)* *Frequency (II)* *Midpoint (III)* *Relative Frequency (IV)* *Cumulative Frequency (V)* A: *I*: *__* - *___* *II*: *_* *III*: *__* *IV*: *____* *V*: *_* B: *I*: *___* - *___* *II*: *_* *III*: *___* *IV*: *____* *V*: *__* C: *I*: *___* - *___* *II*: *_* *III*: *___* *IV*: *____* *V*: *__* D: *I*: *___* - *___* *II*: *_* *III*: *___* *IV*: *____* *V*: *__* E: *I*: *___* - *___* *II*: *__* *III*: *___* *IV*: *____* *V*: *__* F: *I*: *___* - *___* *II*: *_* *III*: *___* *IV*: *____* *V*: *__* *Part 2:* Which class has the greatest frequency? The class with the greatest frequency is from *__(1)__* to *__(2)__*. *Part 3:* Which class has the least frequency? The class with the least frequency is from *__(1)__* to *__(2)__*.
Correct Answers: *Part 1* (*I*; *II*; *III*; *IV*; *V*): A: *30*-*114*; *4*; *72*; *0.138*; *4* B: *115*-*199*; *6*; *157*; *0.207*; *10* C: *200*-*284*; *2*; *242*; *0.069*; *12* D: *285*-*369*; *3*; *327*; *0.103*; *15* E: *370*-*454*; *10*; *412*; *0.345*; *25* F: *455*-*539*; *4*; *497*; *0.138*; *29* *Part 2:* *(1):* *120* *(2):* *199* *Part 3:* *(1):* *40* *(2):* *119* (*2.1.30*)
The distribution of the number of hours that a random sample of people spend doing chores per week is shown in the pie chart. Use 32 as the midpoint for "30+ hours." Make a frequency distribution for the data. Then use the table to estimate the sample mean and the sample standard deviation of the data set. (Since I don't have Quizlet+, I can't insert the actual image of the circle graph; ergo, I pasted the description.) A circle graph entitled *"Weekly Chore Hours"* is divided into *seven sectors* with *labels* and *approximate sizes* as follows: *(0-4 hours: 4 people); (5-9 hours: 13 people); (10-14 hours: 22 people); (15-19 hours: 18 people); (20-24 hours: 14 people); (25-29 hours: 12 people); (30+ hours: 4 people)*. *Part 1:* First construct the frequency distribution. *Class* = *Frequency, f* 0-4 = *_(1)_* 5-9 = *__(2)__* 10-14 = *__(3)__* 15-19 = *__(4)__* 20-24 = *__(5)__* 25-29 = *__(6)__* 30+ = *_(7)_* *Part 2:* Find an approximation for the sample mean. (Type answer as either an *integer* or a *decimal* rounded to the *nearest tenth* (*one* decimal place).) *x̄* = *___* *Part 3:* Find an approximation for the sample standard deviation. (Type answer as either an *integer* or a *decimal* rounded to the *nearest tenth* (*one* decimal place).) s = *__*
Correct Answers: *Part 1:* *(1):* *4* *(2):* *13* *(3):* *22* *(4):* *18* *(5):* *14* *(6):* *12* *(7):* *4* *Part 2:* *16.4* *Part 3:* *7.8* (*2.4.42*)
The estimated distribution (in millions) of the population by age in a certain country for the year 2015 is shown in the pie chart. Make a frequency distribution for the data. Then use the table to estimate the sample mean and the sample standard deviation of the data set (round answers to *two* decimal places). Use 70 as the midpoint for "65 years and over." (Since I don't have Quizlet+, I can't insert the actual image of the circle graph; ergo, I pasted the description.) An untitled circle graph is divided into *eight sectors* with *labels* and *approximate sizes* as follows: *(Under 4 years: 24.3); (5-14 years: 39.2); (15-19 years: 22.9); (20-24 years: 24.5); (25-34 years: 47.7); (35-44 years: 37.1); (45-64 years: 75.4); (65 years and over: 50.4)*. *Part 1:* The sample mean is *x̄* = *____*. *Part 2:* The sample standard deviation is s = *____*.
Correct Answers: *Part 1:* *36.89* *Part 2:* *21.99* (*2.4.41*)
The ogive represents the heights of males in a particular country in the 20-29 age group. What height represents the 60th percentile? How should you interpret this? (Since I don't have Quizlet+, I can't insert the actual image of the ogive; ergo, I pasted the description.) An Ogive has a *horizontal axis* labeled *"Height (in inches)"* from *63 to 76* in *increments of "1"*, and a vertical axis labeled *"Percentile"* from *0 to 100* in *increments of "10"*. The graph consists of fourteen plotted points connected by line segments from left to right. The coordinates of the plotted points are at: *(63, 0), (64, 6), (65, 9), (66, 12), (67, 19), (68, 35), (69, 43), (70, 62), (71, 71), (72, 81), (73, 89), (74, 92), (75, 96)*, and *(76, 100)*. *Part 1:* The 60th percentile represents about *__* inches. (Round answer to the *nearest whole number* (*zero* decimal places).) *Part 2:* Interpret this percentile. Choose the correct answer below. A.) This means that about 60 percent of males in this country ages 20-29 are shorter than this height. B.) This means that about 60 percent of males in this country ages 20-29 are exactly this height. C.) This means that about 60 percent of males in this country ages 20-29 are taller than this height. D.) This means that about 40 percent of males in this country ages 20-29 are shorter than this height.
Correct Answers: *Part 1:* *69* *Part 2:* A.) This means that about 60 percent of males in this country ages 20-29 are shorter than this height. (*2.5.29*)
The ogive represents the heights of males in a particular country in the 20-29 age group. What percentile is a height of 74 inches? How should you interpret this? (Since I don't have Quizlet+, I can't insert the actual image of the ogive; ergo, I pasted the description.) An Ogive has a *horizontal axis* labeled *"Height (in inches)"* from *63 to 76* in *increments of "1"*, and a *vertical axis* labeled *"Percentile"* from *0 to 100* in *increments of "10"*. The graph consists of fourteen plotted points connected by line segments from left to right. The coordinates of the plotted points are at: *(63, 0), (64, 6), (65, 9), (66, 13), (67, 20), (68, 36), (69, 43), (70, 60), (71, 71), (72, 80), (73, 91), (74, 93), (75, 97)*, and *(76, 100)*. *Part 1:* The height of 74 inches is about the *____* percentile. *Part 2:* Interpret what this percentile value means. Choose the correct answer below. A.) This means that the percentage below this percentile value is the percentage of males in this country ages 20-29 that are taller than 74 inches. B.) This means that the percentage below this percentile value is the percentage of males in this country ages 20-29 that are shorter than 74 inches. C.) This means that the percentage below this percentile value is the percentage of males in this country ages 20-29 that are exactly 74 inches. D.) This means that the percentage above this percentile value is the percentage of males in this country ages 20-29 that are shorter than 74 inches.
Correct Answers: *Part 1:* *93rd* *Part 2:* B.) This means that the percentage below this percentile value is the percentage of males in this country ages 20-29 that are shorter than 74 inches. (*2.5.31*)
What are some benefits of representing data sets using frequency distributions? What are some benefits of using graphs of frequency distributions? *Part 1:* What are some benefits of representing data sets using frequency distributions? A.) Organizing the data into a frequency distribution can make patterns within the data more evident. B.) Organizing the data into a frequency distribution makes it possible to graph quantitative data. C.) It is easier to determine the minimum and maximum values of a data set when it has been arranged into a frequency distribution. *Part 2:* What are some benefits of using graphs of frequency distributions? A.) Graphing a frequency distribution makes it possible to determine the relative frequencies of each of the classes. B.) Graphing a frequency distribution makes it possible to find the total number of observations. C.) It can be easier to identify patterns of a data set by looking at a graph of the frequency distribution. D.) It can be easier to determine the class boundaries by looking at a graph of the frequency distribution.
Correct Answers: *Part 1:* A.) Organizing the data into a frequency distribution can make patterns within the data more evident. *Part 2:* C.) It can be easier to identify patterns of a data set by looking at a graph of the frequency distribution. (*2.1.1*)
Find the mean, median, and mode of the data, if possible. If any of these measures cannot be found or a measure does not represent the center of the data, explain why. A sample of seven admission test scores for a professional school are listed below. *11.4 10.3 11.9 10.3 10.4 10.3 11.7* *Part 1:* What is the mean score? Select the correct choice below and fill in any answer box to complete your choice. (Round answer to *one* decimal place.) A.) The mean score is *___*. B.) There is no mean score. *Part 2:* Does the mean represent the center of the data? A.) The mean represents the center. B.) The mean does not represent the center because it is the largest data value. C.) The mean does not represent the center because it is the smallest data value. D.) The mean does not represent the center because it is not a data value. *Part 3:* What is the median score? Select the correct choice below and fill in any answer box to complete your choice. (Round answer to *one* decimal place.) A.) The median score is *___*. B.) There is no median score. *Part 4:* Does the median represent the center of the data? A.) The median represents the center. B.) The median does not represent the center because it is not a data value. C.) The median does not represent the center because it is the smallest data value. D.) The median does not represent the center because it is the largest data value. *Part 5:* What is the mode of the scores? Select the correct choice below and fill in any answer box to complete your choice. (Round answer to *one* decimal place, and use a *comma* to separate answers (if needed).) A.) The mode(s) of the scores is (are) *___*. B.) There is no mode. *Part 6:* Does (Do) the mode(s) represent the center of the data? A.) The mode(s) represent(s) the center. B.) The mode(s) can't represent the center because it (they) is (are) not a data value. C.) The mode(s) does (do) not represent the center because it (one) is the smallest data value. D.) The mode(s) does (do) not represent the center because it (one) is the largest data value.
Correct Answers: *Part 1:* A.) The mean is *10.9*. *Part 2:* A.) The mean represents the center. *Part 3:* A.) The median is *10.4*. *Part 4:* A.) The median represents the center. *Part 5:* A.) The mode(s) is/are *10.3*. *Part 6:* C.) The mode(s) does (do) not represent the center because it (one) is the smallest data value. (*2.3.18*)
The number of credits being taken by a sample of 13 full-time college students are listed below. Find the mean, median, and mode of the data, if possible. If any measure cannot be found or does not represent the center of the data, explain why. *5 7 8 8 5 4 4 4 6 4 4 4 5* *Part 1:* Find the mean. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (Type answer as either an *integer* or a *decimal* rounded to *one* decimal place.) A.) The mean is *__*. B.) The data set does not have a mean. *Part 2:* Does the mean represent the center of the data? A.) The mean represents the center. B.) The mean does not represent the center because it is the largest data value. C.) The mean does not represent the center because it is not a data value. D.) The mean does not represent the center because it is the smallest data value. E.) The data set does not have a mean. *Part 3:* Find the median. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (Type answer as either an *integer* or a *decimal* rounded to *one* decimal place.) A.) The median is *_*. B.) The data set does not have a median. *Part 4:* Does the median represent the center of the data? A.) The median represents the center. B.) The median does not represent the center because it is the largest data value. C.) The median does not represent the center because it is the smallest data value. D.) The median does not represent the center because it is not a data value. E.) The data set does not have a median. *Part 5:* Find the mode. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (Type answer(s) as either an *integer* or a *decimal* rounded to *one* decimal place, and use a *comma* to separate answers (if needed).) A.) The mode(s) is/are *_*. B.) The data set does not have a mode. *Part 6:* Does (Do) the mode(s) represent the center of the data? A.) The mode(s) represent(s) the center. B.) The mode(s) does (do) not represent the center because it (they) is (are) not a data value. C.) The data set does not have a mode. D.) The mode(s) does (do) not represent the center because it (one) is the largest data value. E.) The mode(s) does (do) not represent the center because it (one) is the smallest data value.
Correct Answers: *Part 1:* A.) The mean is *5.2*. *Part 2:* A.) The mean represents the center. *Part 3:* A.) The median is *5*. *Part 4:* A.) The median represents the center. *Part 5:* A.) The mode(s) is/are *4*. *Part 6:* E.) The mode(s) does (do) not represent the center because it (one) is the smallest data value. (*2.3.17*)
Explain how to find the range of a data set. What is an advantage of using the range as a measure of variation? What is a disadvantage? *Part 1:* Explain how to find the range of a data set. Choose the correct answer below. A.) The range is found by adding the minimum and maximum data entries. B.) The range is found by adding the first and last data entries. C.) The range is found by subtracting the minimum data entry from the maximum data entry. D.) The range is found by subtracting the first data entry from the last data entry. *Part 2:* What is an advantage of using the range as a measure of variation? A.) It uses all entries from the data set. B.) It uses only two entries from the data set. C.) It is easy to compute. *Part 3:* What is a disadvantage of using the range as a measure of variation? A.) It uses all entries from the data set. B.) It is hard to compute. C.) It uses only two entries from the data set.
Correct Answers: *Part 1:* C.) The range is found by subtracting the minimum data entry from the maximum data entry. *Part 2:* C.) It is easy to compute. *Part 3:* C.) It uses only two entries from the data set. (*2.4.1*)
Construct the described data set. The entries in the data set cannot all be the same. *The median and the mode are the same.* *Part 1:* What is the definition of median? A.) The sum of the data entries divided by the number of entries. B.) The data entry that occurs with the greatest frequency. C.) The data entry that is far removed from the other entries in the data set. D.) The value that lies in the middle of the data when the data set is ordered. *Part 2:* What is the definition of mode? A.) The value that lies in the middle of the data when the data set is ordered. B.) The data entry that occurs with the greatest frequency. C.) The data entry that is far removed from the other entries in the data set. D.) The sum of the data entries divided by the number of entries. *Part 3:* Choose the data set where the median and mode of the set are equal. A.) 3, 3, 11, 11 B.) 3, 6, 9, 12, 12, 15 C.) 2, 2, 2, 3, 4, 4, 4 D.) 1, 1, 5, 5, 5, 6, 6 *Part 4:* A data set includes the entries 3, 5, 6, 8, 8, and 11. Complete the data set with an entry between 1 and 11 so that the median and mode of the set are equal. (Type answer as either an *integer* or a *decimal*.) *_*
Correct Answers: *Part 1:* D.) The value that lies in the middle of the data when the data set is ordered. *Part 2:* B.) The data entry that occurs with the greatest frequency. *Part 3:* D.) 1, 1, 5, 5, 5, 6, 6 *Part 4:* *9* (*2.3.5*)
