Stat 200 exam 2
Use the Empirical Rule. The mean speed of a sample of vehicles along a stretch of highway is 63 miles per hour, with a standard deviation of 4 miles per hour. Estimate the percent of vehicles whose speeds are between 51 miles per hour and 75 miles per hour. (Assume the data set has a bell-shaped distribution.) Approximately ________% of vehicles travel between 51 miles per hour and 75 miles per hour.
97%
After constructing a relative frequency distribution summarizing IQ scores of college students, what should be the sum of the relative frequencies?
If percentages are used, the sum should be 100%. If proportions are used, the sum should be 1.
Why should the number of classes in a frequency distribution be between 5 and 20?
If the number of classes in a frequency distribution is not between 5 and 20, it may be difficult to detect any patterns.
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? Explain how to find the range of a data set. Choose the correct answer below.
The range is found by subtracting the minimum data entry from the maximum data entry. -------------------- What is an advantage of using the range as a measure of variation? It is easy to compute. ------------------------ disadvantage? It uses only two entries from the data set.
The ages of the winners of a cycling tournament are approximately bell-shaped. The mean age is 28.3 years, with a standard deviation of 3.4 years. The winner in one recent year was 32 years old. (a) Transform the age to a z-score. (b) Interpret the results. (c) Determine whether the age is unusual.
z = (value-mean)/SD= 1.09 1.09 above the mean No comma this value is not unusual. A z-score between minus 2 and 2 is not unusual.
Heights of men on a baseball team have a bell-shaped distribution with a mean of 175 cm and a standard deviation of 7 cm. Using the empirical rule, what is the approximate percentage of the men between the following values? a. 154 cm and 196 cm b. 168 cm and 182 cm a.) _________% of the men are between 154 cm and 196 cm. b.) __________% of the men are between 168 cm and 182 cm.
a.) 99.7% b.)68%
The weights, in pounds, of packages on a delivery truck are shown in the stem-and-leaf plot. Find the mean, the median, and the mode of the data, if possible. If any measure cannot be found or does not represent the center of the data, explain why.
mean: 30 center of data ------------------ median:32.5 center of data ----------------- mode: 22,35 not represent a typical data set
(a) Find the five-number summary, and (b) draw a box-and-whisker plot of the data. 4 8 8 5 1 9 8 7 9 5 9 4 1 6 2 9 8 7 7 9 min: q1: q2: q3: max:
min: 1 q1:4.5 q2:7 q3: 8.25 max: 9
Determine whether the statement is true or false. If it is false, rewrite it as a true statement. The second quartile is the median of an ordered data set.
true
A student's score on an actuarial exam is in the 78th percentile. What can you conclude about the student's exam score?
The student scored higher than 78% of the students who took the actuarial exam.
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.
The shape of the distribution is skewed right because the bars have a tail to the right.
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.
The shape of the distribution is uniform because the bars are approximately the same height.
The data set below represents the ages of 36 executives. Find the percentile that corresponds to an age of 64 years old. 28 29 34 34 34 39 39 41 42 44 46 46 46 46 47 48 49 50 50 52 53 54 56 56 59 60 61 61 62 62 62 63 64 64 64 65
# before 64/ total #
The depths (in inches) at which 10 artifacts are found are listed. Complete parts (a) and (b) below. 24.1 39.8 30.8 31.2 46.6 28.2 30.9 27.1 30.2 34.8
22.5 -------------------- Change 46.6 to 65.3 and find the range of the new data set. 41.2
Use the frequency polygon to identify the class with the greatest, and the class with the least, frequency.
29.3-32.5 What are the boundaries of the class with the least frequency? 11.5-14.5
What are some benefits of representing data sets using frequency distributions? What are some benefits of using graphs of frequency distributions? What are some benefits of representing data sets using frequency distributions?
Organizing the data into a frequency distribution can make patterns within the data more evident.
Use the given frequency distribution to find the (a) class width. (b) class midpoints. (c) class boundaries.
class width: 36-32 = 4 ------------------------------------ Midpoint: ((lower class limit) + (upper class limit)) / 2 32-35: (32+35)/2 = 33.5 36-39: (36 + 39)/2 = 37.5 40-43: 41.5 44-47: 45.5 48-51: 49.5 52-55: 53.5 56-59: 57.5 --------------------------------------- Class boundries: Lower class limit − 0.5 Upper class limit + 0.5 32-35: 31-.5, 35+.5 = 31.5, 35.5 36-39: 35.5, 39.5 40-43: 39.5, 43.5 44-47: 43.5, 47.5 48-51: 47.5, 51.5 52-55: 51.5, 55.5 56-59: 55.5, 59.5
(a) Find the five-number summary, and (b) draw a box-and-whisker plot of the data. 4 8 8 5 2 9 8 7 9 6 9 4 2 6 2 9 8 7 7 9
min: 2 q1: 4.5 q2:7 q3:8.5 max:9
(a) Find the five-number summary, and (b) draw a box-and-whisker plot of the data. 3 8 8 6 2 9 8 7 9 6 9 3 1 6 2 9 8 7 7 9
min= 1 q1 = (n+1 / 4)th value of the observation = 4.5 q2=7 q3=8.5 max= 9
The midpoints A, B, and C are marked on the histogram. Match them to the indicated scores. Which scores, if any, would be considered unusual?
point A: -1.42 B: 0 c = 2.13 unusual= 2.13
The data set below represents the ages of 36 executives. Find the percentile that corresponds to an age of 34 years old.
17
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.
true
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.
The shape of the distribution is skewed left because the bars have a tail to the left.
Why is the standard deviation used more frequently than the variance?
The units of variance are squared. Its units are meaningless.
How is a Pareto chart different from a standard vertical bar graph?
The bars are positioned in order of decreasing height with the tallest bar on the left.
The depths (in inches) at which 10 artifacts are found are listed. 31.4 35.5 33.2 34.1 44.7 29.1 23.8 32.8 23.9 24.7 The range of the given data set is 20.9. If the current maximum, 44.7, is replaced with 51.1, the range then becomes 27.3. Compare these values and determine how outliers affect the range of a data set. How does changing the maximum value affect the range?
The range is greatly affected by this change.
What is the difference between a frequency polygon and an ogive?
A frequency polygon displays class frequencies while an ogive displays cumulative frequencies.
Determine whether the statement is true or false. If it is false, rewrite it as a true statement. In a frequency distribution, the class width is the distance between the lower and upper limits of a class.
False. In a frequency distribution, the class width is the distance between the lower or upper limits of consecutive classes.
Describe the relationship between quartiles and percentiles. ___________ are special cases of _________________ _________ is the 25th percentile, ________ is the 50th percentile, and _________ is the 75th percentile
QUARTILES are special cases of PERCENTILES. Q1 is the 25th percentile, Q2 is the 50th percentile, and Q3 is the 75th percentile
Match the plot with a possible description of the sample.
time (in minutes)it takes people to get to work
Use the frequency distribution shown below to construct an expanded frequency distribution. High Temperatures (degrees F) (sample size= add all frequencies) =365
Frequency 18 (class 20-30) Midpoint: (20+30)/2 = 25 Relative frequency: (class frequency/sample size) 18/365 = .05 cumulative frequency: the frequency +all before frequency = 18 ----------------------------------- Frequency 41 (class 31-41) Midpoint: 36 Relative frequency: .11 cumulative frequency: 18+41 =59 ------------------------------------ Frequency 68 Midpoint: 47 Relative frequency: .19 cumulative frequency: 127
Give conclusions that can be drawn from the graph. Select all the conclusions that can be drawn from the graph.
Too-cautious drivers irk drivers the least Tailgaters irk drivers the most
Determine whether the statement is true or false. If it is false, rewrite it as a true statement. Class boundaries ensure that consecutive bars of a histogram touch.
True
Determine whether the statement is true or false. If it is false, rewrite it as a true statement. The midpoint of a class is the sum of its lower and upper limits divided by two.
the statement is true
Use the ogive to answer parts a) through d). a) What is the cumulative frequency for a weight of 27.5 pounds? b) What is the weight for which the cumulative frequency is 45? c)How many beagles weigh between 22.5 and 29.5 pounds? d) How many beagles weigh more than 30.5 pounds?
a.) 40 (follow line upand over) b.) 30.5 (follow over and down) c.) 37 (subtract bottom number from higher number) d.) 10 (subtract lower number from final number)
The scores and their percent of the final grade for a statistics student are given. What is the student's weighted mean score?
sc % weighted 84 10 8.4 84 15 12.6 96 15 14.4 100 25 25 91 35 31.85 weighted mean: 92.25
Both data sets have a mean of 165. One has a standard deviation of 16, and the other has a standard deviation of 24. Which data set has which deviation? key: 12|8= 128
(a) has a standard deviation of 24 and (b) has a standard deviation of 16, because the data in (a) have more variability.
The scores and their percents of the final grade for a statistics student are given. An error occurred grading the final exam. Instead of getting 93, the student scored 87. What is the student's new weighted mean?
87.1
Use the box-and-whisker plot to determine if the shape of the distribution represented is symmetric, skewed left, skewed right, or none of these.
skewed right
Determine whether the statement is true or false. If it is false, rewrite it as a true statement. A data set can have the same mean, median, and mode.
true
What is the difference between class limits and class boundaries?
Class limits are the least and greatest numbers that can belong to the class. Class boundaries are the numbers that separate classes without forming gaps between them. For integer data, the corresponding class limits and class boundaries differ by 0.5.
You are applying for a job at two companies. Company A offers starting salaries with mu equals $ 34 comma 000 and sigma equals $ 3 comma 000. Company B offers starting salaries with mu equals $ 34 comma 000 and sigma equals $ 7 comma 000. From which company are you more likely to get an offer of $40 comma 000 or more?
Company B, because data values that lie within one standard deviation from the mean are considered very usual.
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. 9 9 12 12 9 10 8 8 8 8 8 8 11
Find the mean. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. 8 8 8 8 8 8 9 9 9 10 11 12 12 mean: 9.2 --------------- Does the mean represent the center of the data? The mean represents the center. ---------------- median: 9 Does the median represent the center of the data? The median represents the center. ------------------- mode: 8 The mode(s) does (do) not represent the center because it (one) is the smallest data value.
What are some benefits of representing data sets using frequency distributions? What are some benefits of using graphs of frequency distributions? What are some benefits of using graphs of frequency distributions?
It can be easier to identify patterns of a data set by looking at a graph of the frequency distribution.
Determine whether the statement is true or false. If it is false, rewrite it as a true statement. It is impossible to have a z-score of 0.
The statement is false. A z-score of 0 is a standardized value that is equal to the mean.
Use the frequency histogram to complete the following parts. (a) Identify the class with the greatest, and the class with the least, relative frequency. (b) Estimate the greatest and least relative frequencies. (c) Describe any patterns with the data.
a: 40.5 bar so 39.5- 41.5 (find average from bar before and bar after) b. 48.5 bar; 47.5-49.5 c. .25 d. .01 sample size (n) = 395 (add all x axis)
A student receives the following grades, with an A worth 4 points, a B worth 3 points, a C worth 2 points, and a D worth 1 point. What is the student's weighted mean grade point score? B in 3 three-credit classes D in 1 three-credit class A in 1 four-credit class C in 1 four-credit class
mean = 2.7
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. 9.6 9.6 9.6 9.7 10.4 10.6 10.9
mean: 10.7 center ------------ median:9.7 center -------------- mode: 9.6 The mode(s) does (do) not represent the center because it (one) is the smallest data value.
Find the range of the data set represented by the graph. "womens age at first childbirth"
range = 10
Determine whether the statement is true or false. If it is false, rewrite it as a true statement. When each data class has the same frequency, the distribution is symmetric.
true
rule for SD distributions %
For data sets with distributions that are approximately symmetric and bell-shaped, the Empirical Rule states that about 68% of the data lie within one standard deviation of the mean, about 95% of the data lie within two standard deviations of the mean, and about 99.7% of the data lie within three standard deviations of the mean.
Determine whether the statement is true or false. If it is false, rewrite it as a true statement. An ogive is a graph that displays relative frequencies.
The statement is false. An ogive is a graph that displays cumulative frequencies.
Given a data set, how do you know whether to calculate sigma or s?
When given a data set, one would have to determine if it represented the population or if it was a sample taken from the population. If the data are a population, then sigma is calculated. If the data are a sample, then s is calculated.
Construct the described data set. The entries in the data set cannot all be the same. The median and the mode are the same.
definition of median: The value that lies in the middle of the data when the data set is ordered. ---------------- mode: The data entry that occurs with the greatest frequency. ----------------------- median and mode are equal: 1,1,8,8,8,9,9 ---------------------- A data set includes the entries 3, 5, 7, 9, 9, and 12. Complete the data set with an entry between 1 and 12 so that the median and mode of the set are equal. 9
The number of hospital beds in a sample of 20 hospitals is shown below. Construct a frequency distribution and a frequency histogram for the data set using 5 classes. Describe the shape of the histogram as symmetric, uniform, negatively skewed, positively skewed, or none of these. 166 160 126 133 176 157 170 220 149 132 193 204 151 251 267 241 306 142 207 181
Construct a frequency distribution for the data set using 5 classes. ------------------- class freq 126-162 8 163-199 5 200-236 3 237-273 3 274-310 1 --------------------- Describe the shape of the histogram as symmetric, uniform, negatively skewed, positively skewed, or none of these. Choose the correct answer below. The histogram is negatively skewed because the left tail is longer than the right tail.
Construct a frequency distribution and a relative frequency histogram for the accompanying data set using five classes. Which class has the greatest relative frequency and which has the least relative frequency? Complete the table below. Use the minimum data entry as the lower limit of the first class.
SumF = 26 class freq relfrq 138-202 14 .538 203-267 4 .154 268-332 4 .154 333-397 1 .038 398-462 3 .115 --------------------- Choose the correct relative frequency histogram below. c graph ---------------- Class has the greatest relative frequency: 138-202 class has the least relative frequency:333-397
Explain the relationship between variance and standard deviation. Can either of these measures be negative? Explain.
The standard deviation is the positive square root of the variance. The standard deviation and variance can never be negative. Squared deviations can never be negative.
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.
The statement is false. All quantitative data set have medians.
The letters A, B, and C are marked on the histogram. Describe the shape of the data. Then determine which is the mean, which is the median, and which is the mode. Justify your answers.
Which description below best describes the shape of the distribution? skewed right ---------------- In this distribution, how is the mode determined? highest frequency ------------------------ mode = A -------------------- In this distribution, how is the mean determined? to the right of median and mode ----------------------- mean = C --------------------- In this distribution, how is the median determined? The median is to the left of the mean and to the right of the mode. ------------------------ Median = B
What is the difference between relative frequency and cumulative frequency?
Relative frequency of a class is the percentage of the data that falls in that class, while cumulative frequency of a class is the sum of the frequencies of that class and all previous classes.
The ogive represents the heights of males in a particular country in the 20-29 age group. What height represents the 70th percentile? How should you interpret this?
70th percentile is about = 71 Interpret this percentile. Choose the correct answer below. = This means that about 70 percent of males in this country ages 20-29 are shorter than this height.
A certain brand of automobile tire has a mean life span of 39 comma 000 miles and a standard deviation of 2 comma 350 miles. (Assume the life spans of the tires have a bell-shaped distribution.) (a) The life spans of three randomly selected tires are 34 comma 000 miles, 38 comma 000 miles, and 31 comma 000 miles. Find the z-score that corresponds to each life span.
34= -2.13 38= -.43 31= -3.40 unusual = yes 36650: z = -1=16% 41350: z=1 = 84% 39000: 50%
Use the ogive to approximate (a) the number in the sample, (b) the location of the greatest increase in frequency.
a) 50 b) 22.5-23.5
The data show the number of hours spent studying per day by a sample of 28 students. Use the box-and-whisker plot below to answer parts (a) through (c) below. 1 11 5 4 3 0 5 9 6 1 7 4 6 3 1 1 1 9 6 5 2 4 9 2 0 9 3 8
About 75% of the students studied no more than how many hours per day? = 6.5 What percent of the students studied more than 4 hours per day? 50% You randomly select one student from the sample. What is the likelihood that the student studied less than 1.5 hours per day? = 25%
Use the dot plot to list the actual data entries. What is the maximum data entry? What is the minimum data entry?
Choose the correct actual data entries below. 18, 18, 19, 19, 19, 20, 20, 20, 20, 20, 21, 22, 22, 23, 24 ------------- max: 24 min:18
Use the stem-and-leaf plot to list the actual data entries. What is the maximum data entry? What is the minimum data entry?
Choose the correct actual data entries below. 26, 32, 41, 43, 43, 45, 46, 46, 47, 50, 51, 51, 52, 53, 53, 53, 54, 54, 54, 54, 55, 56, 56, 58, 59, 67, 67, 67, 73, 77, 77, 83 --------------------- max: 83 min: 26
The accompanying data set lists the numbers of children of world leaders. Use the data to construct a frequency distribution using six classes and to create a frequency polygon. Describe any patterns.
Class Freq mid 0-2 11 1 3-5 13 4 6-8 11 7 9-11 1 10 12-14 2 13 15-17 5 16 ------------------------ Create a frequency polygon. Choose the correct graph below. graph c ------------------------ Describe any patterns. Choose the correct answer below. The data show that most of the 43 world leaders had fewer than 6 children.
The class levels of 32 students in a physics course are shown below. Find the mean, median, and mode of the data, if possible. If any measure cannot be found, explain why. freshman:10 sophmore: 12 junior: 8 senior: 2
Find the mean. Select the correct choice below and, if necessary, fill in the answer box to complete your choice: The mean cannot be calculated because the data are at the nominal level of measurement. ------------ Does the mean represent the center of the data? data does not have a mean ------------ median: The median cannot be calculated because the data are at the nominal level of measurement. no median --------------- mode: sophmores Yes, the mode represents a typical data entry.
The ages of the winners of a cycling tournament are approximately bell-shaped. The mean age is 27.9 years, with a standard deviation of 3.3 years. The winner in one recent year was 34 years old. (a) Transform the age to a z-score. (b) Interpret the results. (c) Determine whether the age is unusual.
z=1.85 1.85 above the mean No comma this value is not unusual. A z-score between minus 2 and 2 is not unusual.
The data set below represents the ages of 30 executives. Which ages are above the 75th percentile? 44 59 64 47 57 40 56 54 60 55 56 50 66 56 50 60 48 40 49 44 55 40 48 45 29 34 39 42 41 44
The ages above the 75th percentile are 57 comma 59 comma 60 comma 60 comma 64 comma 66.
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= 12, maximum=81, 7 classes
The class width: (81- 12)/ 7 = 10 The lower class limits are: minimum + class width = 12,22,32,42,52,62,72 The upper class limits are: (begin at 1 less thaan the second lower class then add class width) = 21,31,41,51,61,71,81
Without performing any calculations, determine which measure of central tendency best represents the graphed data. Explain your reasoning.
The mean is the best measure because there are outliers and the data is skewed.
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.
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.
Determine whether the statement is true or false. If it is false, rewrite it as a true statement. The 50th percentile is equivalent to Upper Q 1.
The statement is false. The 50th percentile is equivalent to Upper Q 2.
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?
The team scored fewer goals per game than 75% of the teams in the league.
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.
What is the definition of mean?: The sum of the data entries divided by the number of entries. --------------------- Choose the data set whose mean is not equal to a value in the set. 5,5,6,6
Describe the difference between the calculation of population standard deviation and that of sample standard deviation. Let N be the number of data entries in a population and n be the number of data entries in a sample data set. Choose the correct answer below.
When calculating the population standard deviation, the sum of the squared deviation is divided by N, then the square root of the result is taken. When calculating the sample standard deviation, the sum of the squared deviations is divided by nminus1, then the square root of the result is taken.
The mean value of land and buildings per acre from a sample of farms is $1800, with a standard deviation of $100. The data set has a bell-shaped distribution. Using the empirical rule, determine which of the following farms, whose land and building values per acre are given, are unusual (more than two standard deviations from the mean). Are any of the data values very unusual (more than three standard deviations from the mean)? $1861 $2085 $1754 $1498 $1919 $1856 a.) Which of the farms are unusual (more than two standard deviations from the mean)? Select all that apply. b.) Which of the farms are very unusual (more than three standard deviations from the mean)? Select all that apply.
a.) $2085 and $1498 b.)$1498
The table shows population statistics for the ages of Best Actor and Best Supporting Actor winners at an awards ceremony. The distributions of the ages are approximately bell-shaped. Compare the z-scores for the actors in the following situation. Best Actor Best Supporting Actor muequals44.0 muequals50.0 sigmaequals6.9 sigmaequals14 In a particular year, the Best Actor was 41 years old and the Best Supporting Actor was 81 years old.
best actor: z= -.41 best supporting: z = 2.21 The Best Actor was less than 1 standard deviation below the mean, which is not unusual. The Best Supporting Actor was more than 2 standard deviations above the mean, which is unusual.
During a quality assurance check, the actual contents (in grams) of six containers of protein powder were recorded as 1532, 1523, 1498, 1511, 1527, and 1509. (a) Find the mean and the median of the contents. (b) The third value was incorrectly measured and is actually 1512. Find the mean and the median of the contents again. (c) Which measure of central tendency, the mean or the median, was affected more by the data entry error?
mean: 1516.7 median:1517 ------------------ mean:1519 median: 1517.5 ---------------- mean increased by 2.3 and the median increased by .5 so the mean increased more
Use the box-and-whisker plot to identify the five-number summary.
min = 11 q1 = 12 q2=16 q3= 18 max = 20
The ages (in years) of a random sample of shoppers at a gaming store are shown. Determine the range, mean, variance, and standard deviation of the sample data set. 12, 17, 23, 14, 13, 17, 21, 17, 15, 18
range: 11 mean: 16.7 varience:11.79 (SUM(observerd-mean)^2)/n-1 standard deviation: 3.4 sqrrt(varience)
The numbers of regular season wins for 10 football teams in a given season are given below. Determine the range, mean, variance, and standard deviation of the population data set. 2, 7, 15, 4, 11, 6, 14, 9, 3, 9
range: 13 mean: 8 varience: (SUM(observerd-mean)^2)/N 17.8 standard deviation: sqrrt(varience) 4.2
In terms of displaying data, how is a stem-and-leaf plot similar to a dot plot? Select all the similarities below.
- Both plots can be used to identify unusual data values. - Both plots can be used to determine specific data entries. - Both plots show how data are distributed.
Match the plot with a possible description of the sample.
Highest yearly temperature of sample deserts
The mean value of land and buildings per acre from a sample of farms is $1600, with a standard deviation of $100. The data set has a bell-shaped distribution. Assume the number of farms in the sample is 70. a.) Use the empirical rule to estimate the number of farms whose land and building values per acre are between $1400 and $1800. b.) If 26 additional farms were sampled, about how many of these additional farms would you expect to have land and building values between $1400 per acre and $1800 per acre?
a.) 95% of 70 = 67 farms b.)95% of 26 = 25
What is an advantage of using a stem-and-leaf plot instead of a histogram? What is a disadvantage? ------------------- What is a disadvantage of using a stem-and-leaf plot instead of a histogram?
Stem-and-leaf plots contain original data values where histograms do not. ----------------------- Histograms easily organize data of all sizes where stem-and-leaf plots do not.
Use the frequency histogram to complete the following parts. (a) Determine the number of classes. (b) Estimate the greatest and least frequencies. (c) Determine the class width. (d) Describe any patterns with the data.
a: 7 b: 20 c: 275 d: About half of the employees' salaries are between $50,000 and $69,000.
A certain brand of automobile tire has a mean life span of 37 comma 000 miles and a standard deviation of 2 comma 200 miles. (Assume the life spans of the tires have a bell-shaped distribution.) The life spans of three randomly selected tires are 34 comma 000 miles, 38 comma 000 miles, and 31 comma 000 miles. Find the z-score that corresponds to each life span.
34000 mile z = -1.36 38000 mile z = .45 31000 mile z = -2.73 -yes one would be unusual --------------------------------- The life spans of three randomly selected tires are 34 comma 800 miles, 39 comma 200 miles, and 37 comma 000 miles. Using the empirical rule, find the percentile that corresponds to each life span. 34800 %= 16 39200 %= 84 37000 % = 50 (68% 1 SD from mean, 95 2SD and 99.7 3 SD from mean) When a distribution is approximately bell-shaped, the empirical rule says that 68% of the data lie within one standard of the mean, 95% of the data lie within two standard deviations of the mean, and 99.7% of the data lie within three standard deviations of the mean. So, when this distribution's values are transformed to z-scores, about 68% of the z-scores should fall between minus1 and 1, about 95% should fall between minus2 and 2, and about 99.7% should fall between minus3 and 3. Transform each value to a z-score, and use the empirical rule to find the percentage of tires that have a life span at or below each life span.
Use the frequency histogram to complete the following parts. (a) Determine the number of classes. (b) Estimate the greatest and least frequencies. (c) Determine the class width. (d) Describe any patterns with the data.
A) number of classes: 7 (count x axis) B) least frequency: 20 (estemate height of lowest bar) C) Greatest frequency: 300 (height of tallest bar) class width: 37-32 = 5 D) What is the pattern of this histogram? About half of the employees' salaries are between $40,000 and $49,000.
The acccompanying data set lists the retirement ages for 24 doctors. Use the data to construct a cumulative frequency distribution using six classes and to create an ogive for the data set. Then describe the location of the greatest increase in frequency.
class freq cumfre 50-54 2 2 55-59 4 6 60-64 4 10 65-69 9 19 70-74 2 21 75-79 3 24 ------------------- Create an ogive for the data set. Choose the correct graph below. graph D ---------- Where does the greatest increase in cumulative frequency occur? The location of the greatest increase in cumulative frequency is at class 65-69 (plae of largest cumulative frequency
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? Complete the table, starting with the lowest class limit. 19 12 7 10 18 4 11 17 3 11 9 17 8 7 0 5 10 9 1 9
class: 0-3 frequency: 3 midpoint: 1.5 relative frequency:.15 cumulative frequency: 3 ------------------------------- class: 4-7 frequency: 4 midpoint: 5.5 relative frequency: .20 cumulative frequency: 7 ------------------------------- class: 8-11 frequency: 8 midpoint: 9.5 relative frequency:.4 cumulative frequency: 15 ------------------------------- class: 12-15 frequency: 1 midpoint: 13.5 relative frequency:.05 cumulative frequency: 16 ------------------------------- class:16-19 frequency: 4 midpoint: 17.5 relative frequency: .2 cumulative frequency: 20 _________________________________________________ Which class has the greatest frequency? 8-11 ------------------------------------ least frequency? 12-15
