Section 1 Homework
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 image of the actual frequency polygon; ergo, I pasted the description). A frequency polygon titled *Raw MCAT Scores* has a horizontal axis labeled *Score* from 7 to 46 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: *(10, 0); (13, 1); (16, 2); (19, 4); (22, 7); (25, 7); (28, 13); (31, 14); (34, 11); (37, 6); (40, 2); (43, 0)*. *Part 1:* What are the boundaries of the class with the *greatest* frequency? A.) 29.5-32.5 B.) 28.5-33.5 C.) 31-34 D.) 28-34 *Part 2:* What are the boundaries of the class with the *least* frequency? A.) 10-16 B.) 10.5-15.5 C.) 11.5-14.5 D.) 13-16
Correct Answers: *Part 1:* A.) 29.5 - 32.5 *Part 2:* C.) 11.5 - 14.5
What is the difference between class limits and class boundaries? Choose the correct answer below. A.) Class limits are the numbers that separate classes without forming gaps between them. Class boundaries are the least and greatest numbers that can belong to the class. For integer data, the corresponding class limits and class boundaries are the same. B.) 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. C.) Class limits are the numbers that separate classes without forming gaps between them. Class boundaries are the least and greatest numbers that can belong to the class. For integer data, the corresponding class limits and class boundaries differ by 0.5. D.) 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 are the same. E.) Class limits are the numbers that separate classes without forming gaps between them. Class boundaries are the least and greatest numbers that can belong to the class. For integer data, the corresponding class limits and class boundaries differ by 1.
Correct Answer: B.) 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.
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 classes do not overlap. C.) The number of classes in a frequency distribution should be between 5 and 20 so that the class width is not too large. D.) The number of classes in a frequency distribution should be between 5 and 20 so that the class width is not too small. E.) If the number of classes in a frequency distribution is not between 5 and 20, it may be difficult to detect any patterns.
Correct Answer: E.) If the number of classes in a frequency distribution is not between 5 and 20, it may be difficult to detect any patterns.
Use the frequency distribution shown below to construct an expanded frequency distribution (round all answers to the *nearest hundredth* (*two* decimal places)). High Temperatures (°F) *Class* (*A*): 17-27 (*B*): 28-38 (*C*): 39-49 (*D*): 50-60 (*E*): 61-71 (*F*): 72-82 (*G*): 83-93 *Frequency, ƒ* (*A*): 18 (*B*): 41 (*C*): 66 (*D*): 67 (*E*): 84 (*F*): 66 (*G*): 23 Complete the table below. Class (I) Frequency (II) *Midpoint (III)* *Relative Frequency (IV)* *Cumulative Frequency (V)* *A:* I: 17 - 27 II: 18 *III*: *__* *IV*: *___* *V*: *__* *B:* I: 28 - 38 II: 41 *III*: *__* *IV*: *___* *V*: *__* *C:* I: 39 - 49 II: 66 *III*: *__* *IV*: *___* *V*: *___* *D:* I: 50 - 60 II: 67 *III*: *__* *IV*: *___* *V*: *___* *E:* I: 61 - 71 II: 84 *III*: *__* *IV*: *___* *V*: *___* *F:* I: 72 - 82 II: 66 *III*: *__* *IV*: *___* *V*: *___* *G:* I: 83 - 93 II: 23 *III*: *__* *IV*: *___* *V*: *___*
Correct Answers (*III*; *IV*; *V*): *(A):* *22*; *0.05*; *18* *(B):* *33*; *0.11*; *59* *(C):* *44*; *0.18*; *125* *(D):* *55*; *0.18*; *192* *(E):* *66*; *0.23*; *276* *(F):* *77*; *0.18*; *342* *(G):* *88*; *0.06*; *365*
Use the ogive to approximate *Part 1 (a)* the number in the sample, and *Part 2 (b)* the location of the greatest increase in frequency (the graph info is listed below; I can't include the actual graph because I don't have Quizlet+). A line graph, titled *Male Beagles*, with vertical axis, titled *Cumulative Frequency*, starting at 0 going to 55 in increments of 5. The horizontal axis, titled *Weight (in pounds)*, extends from 19.5 to 35.5 in one pound increments. There are 16 plotted points, connected by line segments: *(19.5, 0); (20.5, 2); (21.5, 6); (22.5, 9); (23.5, 10); (24.5, 22); (25.5, 24); (26.5, 29); (27.5, 38); (28.5, 40); (29.5, 44); (30.5, 45); (31.5, 46); (32.5, 48); (33.5, 54); (34.5, 55)*. *Part 1 (a):* The approximate number in the sample is *__*. *Part 2 (b):* Choose the correct location of the greatest increase in frequency below. A.) 20.5-21.5 pounds B.) 27.5-28.5 pounds C.) 33.5-34.5 pounds D.) 23.5-24.5 pounds
Correct Answers: *Part 1 (a):* *55* *Part 2 (b):* D.) 23.5 - 24.5 pounds
You work at a bank and are asked to recommend the amount of cash to put in an ATM each day. You don't want to put in too much (security) or too little (customer irritation). Complete parts 1 (a) through (c) below. *Daily withdrawals (in 100s of dollars) for a period of 30 days:* *52 80 65 57 61 70 69 81 79 64 69 66 57 61 66 62 61 68 63 73 60 65 63 66 69 64 71 58 75 67* *Part 1 (a):* Choose the correct relative frequency histogram for the data using eight classes below (since I don't have Quizlet+, I can't insert the images of the actual histograms; ergo, I have the descriptions). A.) A histogram has a horizontal axis labeled from *48 to 84* in *increments of "4"*, and a vertical axis labeled from *0 to 0.4* in *intervals of "0.05"*. The histogram contains vertical bars of width 4, 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"*: *(52, 0.033); (56, 0.100); (60, 0.233); (64, 0.267); (68, 0.167); (72, 0.100); (76, 0.033); (80, 0.067)*. B.) A histogram has a horizontal axis labeled from *50 to 86* in *increments of "4"*, and a vertical axis labeled from *0 to 0.4* in *intervals of "0.05"*. The histogram contains vertical bars of width 4, 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"*: *(53.5, 0.033); (57.5, 0.100); (61.5, 0.233); (65.5, 0.267); (69.5, 0.167); (73.5, 0.100); (77.5, 0.033); (81.5, 0.067)*. C.) A histogram has a horizontal axis labeled from *52 to 85* in *increments of "4"*, and a vertical axis labeled from *0 to 0.4* in *intervals of "0.05"*. The histogram contains vertical bars of width 4, 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"*: *(56, 0.033); (60, 0.100); (64, 0.233); (68, 0.267); (72, 0.167); (76, 0.100); (80, 0.033); (81, 0.067)*. D.) A histogram has a horizontal axis labeled from *50 to 86* in *increments of "4"*, and a vertical axis labeled from *0 to 0.4* in *intervals of "0.05"*. The histogram contains vertical bars of width 4, 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"*: *(53.5, 0.033); (57.5, 0.100); (61.5, 0.233); (65.5, 0.267); (69.5, 0.167); (73.5, 0.100); (77.5, 0.033); (81.5, 0.067)*. *Part 2 (b):* If you put $7,150 in the ATM each day, what percent of the days in a month should you expect to run out of cash? (Round to the nearest *tenth* (*one* decimal place).) *___%* *Part 3 (c):* If you are willing to run out of cash for 10% of the days, how much cash should you put in the ATM each day? (Round to the nearest *hundred dollars* (*two* decimal places).) *$____*
Correct Answers: *Part 1 (a):* B.) A histogram has a horizontal axis labeled from *50 to 86* in *increments of "4"*, and a vertical axis labeled from *0 to 0.4* in *intervals of "0.05"*. The histogram contains vertical bars of width 4, 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"*: *(53.5, 0.033); (57.5, 0.100); (61.5, 0.233); (65.5, 0.267); (69.5, 0.167); (73.5, 0.100); (77.5, 0.033); (81.5, 0.067)*. *Part 2 (b):* *16.7%* *Part 3 (c):* *$7,500*
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 = 70, 6 classes* *Part 1:* The class width is *__*. *Part 2:* Choose the correct lower class limits below. A.) 22, 31, 42, 52, 62, 71 B.) 12, 22, 32, 42, 52, 62 C.) 21, 31, 42, 51, 61, 71 D.) 12, 21, 32, 41, 51, 62 *Part 3:* Choose the correct upper class limits below. A.) 21, 31, 42, 52, 61, 71 B.) 21, 31, 41, 51, 61, 71 C.) 22, 32, 41, 51, 62, 71 D.) 22, 32, 42, 52, 62, 71
Correct Answers: *Part 1:* *10* *Part 2:* B.) 12, 22, 32, 42, 52, 62 *Part 3:* B.) 21, 31, 41, 51, 61, 71
Construct a frequency distribution and a frequency histogram for the data set using the indicated number of classes. Describe any patterns. *Number of classes: "8"* *Data set: Finishing times (in seconds) of "20" male participants in a 5K race* *1717 1634 1573 1472 2300 1447 1251 1804 1598 1776 1956 1523 1825 1615 1304 1822 2022 2083 1581 1480* *Part 1:* Construct a frequency distribution of the data. Use the minimum data entry as the lower limit of the first class. *Class (I)* *Frequency (II)* 1.) *I:* *____* - *____* *II:* *__* 2.) *I:* *____* - *____* *II:* *__* 3.) *I:* *____* - *____* *II:* *__* 4.) *I:* *____* - *____* *II:* *__* 5.) *I:* *____* - *____* *II:* *__* 6.) *I:* *____* - *____* *II:* *__* 7.) *I:* *____* - *____* *II:* *__* 8.) *I:* *____* - *____* *II:* *__* *Part 2:* Construct a frequency histogram of the data. A.) A frequency histogram has a horizontal axis labeled *"Class"* from *1 to 8* in *increments of "1"*, and a vertical axis labeled *"Frequency"* from *0 to 8* 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"*: *(1, 3); (2, 2); (3, 1); (4, 2); (5, 2); (6, 6); (7, 3); (8, 1)*. B.) A frequency histogram has a horizontal axis labeled *"Class"* from *1 to 8* in *increments of "1"*, and a vertical axis labeled *"Frequency"* from *0 to 8* 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"*: *(1, 1); (2, 1); (3, 2); (4, 3); (5, 2); (6, 6); (7, 3); (8, 2)*. C.) A frequency histogram has a horizontal axis labeled *"Class"* from *1 to 8* in *increments of "1"*, and a vertical axis labeled *"Frequency"* from *0 to 8* 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"*: *(1, 2); (2, 3); (3, 6); (4, 2); (5, 3); (6, 2); (7, 1); (8, 1)*. D.) A frequency histogram has a horizontal axis labeled *"Class"* from *1 to 8* in *increments of "1"*, and a vertical axis labeled *"Frequency"* from *0 to 8* 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"*: *(1, 6); (2, 2); (3, 3); (4, 1); (5, 2); (6, 3); (7, 1); (8, 2)8. *Part 3:* Describe any patterns. Choose the correct answer below. A.) The class with the *greatest frequency* is *class 1*. The class with the *least frequency* is *class 8*. B.) The class with the *greatest frequency* is *class 8*. The class with the *least frequency* is *class 2*. C.) The class with the *greatest frequency* is *class 3*. The classes with the *least frequency* are *classes 7* and *8*. D.) The classes with the *greatest frequency* are *classes 7* and *8*. The class with the *least frequency* is *class 3*.
Correct Answers: *Part 1* (*I*; *II*): 1.) *1251* - *1382*; *2* 2.) *1383* - *1514*; *3* 3.) *1515* - *1646*; *6* 4.) *1647* - *1778*; *2* 5.) *1779* - *1910*; *3* 6.) *1911* - *2042*; *2* 7.) *2043* - *2174*; *1* 8.) *2175* - *2306*; *1* *Part 2:* C.) A frequency histogram has a horizontal axis labeled *"Class"* from *1 to 8* in *increments of "1"* and a vertical axis labeled *"Frequency"* from *0 to 8* 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"*: *(1, 2); (2, 3); (3, 6); (4, 2); (5, 3); (6, 2); (7, 1); (8, 1)*. *Part 3:* C.) The class with the *greatest frequency* is *class 3*. The classes with the *least frequency* are *classes 7* and *8*. INcorrect Answers (in quotes): *Part 1* (*I*; *II*): 8.) *230"7"*
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. *Number of Children*: *1 3 6 1 2 16 6 5 2 2 3 4 1 6 1 5 1 5 0 2 2 7 3 1 6 3 2 5 2 2 6 7 8 2 5 0 1 9 16 10 11 15 13* *Part 1:* Complete the frequency distribution table below. Use the minimum data entry as the lower limit of the first class. *Class (I)* *Frequency (II)* *Midpoint (III)* 1.) *I:* *_* - *_* *II:* *__* *III:* *_* 2.) *I:* *_* - *_* *II:* *__* *III:* *_* 3.) *I:* *_* - *_* *II:* *_* *III:* *_* 4.) *I:* *_* - *__* *II:* *_* *III:* *__* 5.) *I:* *__* - *__* *II:* *_* *III:* *__* 6.) *I:* *__* - *__* *II:* *_* *III:* *__* *Part 2:* Create a frequency polygon. Choose the correct graph below (since I don't have Quizlet+, I can't insert the images of the actual graphs; ergo, I have the descriptions). A.) A frequency polygon has a horizontal axis labeled *"Number of Children"* from *-4 to 21* in *increments of "2"*, and a vertical axis labeled *"Frequency"* from *0 to 22* 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 *"number of children" is listed "first"*, and the *"frequency" is listed "second"*: *(-2, 0); (1, 18); (4, 19.8); (7, 1.8); (10, 6.4); (13, 3); (16, 1); (19, 0)*. B.) A frequency polygon has a horizontal axis labeled *"Number of Children"* from *-3 to 19* in *increments of "2"*, and a vertical axis labeled *"Frequency"* from *0 to 22* 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 *"number of children" is listed "first"*, and the *"frequency" is listed "second"*: *(-2, 0); (1, 18); (4, 10); (7, 8); (10, 3); (13, 1); (16, 3); (19, 0)*. C.) A frequency polygon has a horizontal axis labeled *"Number of Children"* from *-3 to 19* in *increments of "2"*, and a vertical axis labeled *"Frequency"* from *0 to 22* 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 *"number of children" is listed "first"*, and the *"frequency" is listed "second"*: *(-2, 0); (1, 19.8); (4, 10); (7, 4.8); (10, 2.4); (13, 1.1); (16, 3); (19, 0)*. D.) A frequency polygon has a horizontal axis labeled *"Number of Children"* from *-3 to 19* in *increments of "2"*, and a vertical axis labeled *"Frequency"* from *0 to 22* 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 *"number of children" is listed "first"*, and the *"frequency" is listed "second"*: *(-2, 0); (1, 10); (4, 18); (7, 3); (10, 1); (13, 8); (16, 3); (19, 0)*. *Part 3:* Describe any patterns. Choose the correct answer below. A.) The data show that most of the 43 world leaders had more than 17 children. B.) The data show that most of the 43 world leaders had fewer than 6 children. C.) The data show that most of the 43 world leaders had fewer than 2 children. D.) The data show that most of the 43 world leaders had more than 11 children.
Correct Answers: *Part 1* (*I*; *II*; *III*): 1.) *0* - *2*; *18*; *1* 2.) *3* - *5*; *10*; *4* 3.) *6* - *8*; *8*; *7* 4.) *9* - *11*; *3*; *10* 5.) *12* - *14*; *1*; *13* 6.) *15* - *17*; *3*; *16* *Part 2:* B.) A frequency polygon has a horizontal axis labeled *"Number of Children"* from *-3 to 19* in *increments of "2"*, and a vertical axis labeled *"Frequency"* from *0 to 22* 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 *"number of children" is listed "first"*, and the *"frequency" is listed "second"*: *(-2, 0); (1, 18); (4, 10); (7, 8); (10, 3); (13, 1); (16, 3); (19, 0)*. *Part 3:* B.) The data show that most of the 43 world leaders had fewer than 6 children.
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: *281 390 388 446 145 516 199 271 220 173 170 148 178 429 334 243 127 244 40 149 174 225 395 88 151 145 192 444* *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 all answers as either *integers* or *decimals*. Round the *"class limits"* to the *nearest whole number* (*zero* decimal places), but *"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*: *40*-*119*; *2*; *79.5*; *0.069*; *2* *B:* *120*-*199*; *12*; *159.5*; *0.414*; *14* *C:* *200*-*279*; *5*; *239.5*; *0.172*; *19* *D:* *280*-*359*; *3*; *319.5*; *0.103*; *22* *E:* *360*-*439*; *4*; *399.5*; *0.138*; *26* *F:* *440*-*519*; *3*; *479.5*; *0.103*; *29* *Part 2:* *(1):* *120* *(2):* *199* *Part 3:* *(1):* *40* *(2):* *119*
Use the frequency histogram to complete the following parts (since I don't have Quizlet+, I can't insert the image of the actual frequency histogram; ergo, I pasted the description). *Part 1:* Identify the class with the greatest, and the class with the least, relative frequency. (Type both answers as either *integers* or *decimals*, but *DO NOT ROUND*. Use *ascending* order (*least* to *greatest*).) *Part 2:* Estimate the greatest and least relative frequencies. (Round both answers to *two* decimal places.) *Part 3:* Describe any patterns with the data. A frequency histogram titled *Female Fibula Lengths* has a horizontal axis labeled *Length (in centimeters)* from 30.5 to 48.5 in increments of 2 and a vertical axis labeled *Relative Frequency* from 0 to 0.25 in increments of 0.05. The heights of the bars are as follows, with the *length (in centimeters)* first, and the *relative frequency* second (bolded): 30.5 = *0.03* 32.5 = *0.04* 34.5 = *0.05* 36.5 = *0.13* 38.5 = *0.23* 40.5 = *0.25* 42.5 = *0.13* 44.5 = *0.06* 46.5 = *0.07* 48.5 = *0.01* *Part 1:* *(a):* The class with the *greatest* relative frequency is *__[i]__* to *__[ii]__* centimeters. *(b):* The class with the least relative frequency is *__[i]__* to *__[ii]__* centimeters. *Part 2:* *(a):* The greatest relative frequency is about *____*. *(b):* The least relative frequency is about *____*. *Part 3:* Identify one fact that the data show. Choose the correct answer below. A.) About 25% of females have a fibula length between 33.5 and 35.5 centimeters. B.) About two-thirds of females have a fibula length between 41.5 and 49.5 centimeters. C.) About two-thirds of females have a fibula length between 31.5 and 39.5 centimeters. D.) About 25% of females have a fibula length between 39.5 and 41.5 centimeters.
Correct Answers: *Part 1:* *(a):* *[i]:* *39.5* *[ii]:* *41.5* *(b):* *[i]:* *47.5* *[ii]:* *49.5* *Part 2:* *(a):* *0.25* *(b):* *0.01* *Part 3:* D.) About 25% of females have a fibula length between 39.5 and 41.5 centimeters.
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 = 21, maximum = 140, 8 classes* *Part 1:* The class width is *__*. (Type answer as a *whole number* (*zero* decimal places).) *Part 2:* Choose the correct lower class limits below. A.) 36, 50, 66, 81, 96, 110, 125, 140 B.) 21, 35, 51, 65, 80, 96, 110, 126 C.) 21, 36, 51, 66, 81, 96, 111, 126 D.) 35, 50, 66, 80, 95, 110, 126, 140 *Part 3:* Choose the correct upper class limits below. A.) 35, 50, 65, 80, 95, 110, 125, 140 B.) 35, 50, 66, 81, 95, 110, 125, 140 C.) 36, 51, 65, 80, 96, 110, 126, 140 D.) 36, 51, 66, 81, 96, 110, 126, 140
Correct Answers: *Part 1:* *15* *Part 2:* C.) 21, 36, 51, 66, 81, 96, 111, 126 *Part 3:* A.) 35, 50, 65, 80, 95, 110, 125, 140
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 = 8, maximum = 55, 7 classes* *Part 1:* The class width is *_*. (Type answer as a *whole number* (*zero* decimal places).) Use the minimum as the first lower class limit, and then find the remaining lower class limits. (Type answers as *whole numbers* (*zero* decimal places), and use a *comma* to separate answers (if needed).) *Part 2:* The lower class limits are *_, __, __, __, __, __, __*. *Part 3:* The upper class limits are *__, __, __, __, __, __, __*.
Correct Answers: *Part 1:* *7* *Part 2:* *8, 15, 22, 29, 36, 43, 50* *Part 3:* *14, 21, 28, 35, 42, 49, 56*
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 makes it possible to graph quantitative data. B.) Organizing the data into a frequency distribution can make patterns within the data more evident. 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.) It can be easier to identify patterns of a data set by looking at a graph of the frequency distribution. B.) Graphing a frequency distribution makes it possible to determine the relative frequencies of each of the classes. C.) It can be easier to determine the class boundaries by looking at a graph of the frequency distribution. D.) Graphing a frequency distribution makes it possible to find the total number of observations.
Correct Answers: *Part 1:* B.) Organizing the data into a frequency distribution can make patterns within the data more evident. *Part 2:* A.) It can be easier to identify patterns of a data set by looking at a graph of the frequency distribution.
Use the data set listed and technology to create frequency histograms with *5*, *10*, and *20* classes. *2 8 3 1 11 2 14 9 5 10 11 12 9 6 10 10 1 2 11 6 6 4 3 8 15* *Part 1:* Create a histogram with *5* classes. Choose the correct histogram below (since I don't have Quizlet+, I can't insert the images of the actual histograms; ergo, I have the descriptions). A.) A histogram has a horizontal axis labeled *"Data Value"* from *0 to 16* in *increments of "1"*, and a vertical axis labeled *"Frequency"* from *0 to 10* in *increments of "1"*. The histogram has vertical bars of width 3 starting at the horizontal axis value 0.5. The approximate heights of the bars are as follows, where the *"left horizontal axis label" is listed "first"*, and the *"approximate height" is listed "second"*: *(0.5, 3); (3.5, 5); (6.5, 6); (9.5, 3); (12.5, 8)*. B.) A histogram has a horizontal axis labeled *"Data Value"* from *0 to 16* in *increments of "1"*, and a vertical axis labeled *"Frequency"* from *0 to 10* in *increments of "1"*. The histogram has vertical bars of width 3 starting at the horizontal axis value 0.5. The approximate heights of the bars are as follows, where the *"left horizontal axis label" is listed "first"*, and the *"approximate height" is listed "second"*: *(0.5, 4); (3.5, 8); (6.5, 9); (9.5, 8); (12.5, 4)*. C.) A histogram has a horizontal axis labeled *"Data Value"* from *0 to 16* in *increments of "1"*, and a vertical axis labeled *"Frequency"* from *0 to 10* in *increments of "1"*. The histogram has vertical bars of width 3 starting at the horizontal axis value 0.5. The approximate heights of the bars are as follows, where the *"left horizontal axis label" is listed "first"*, and the *"approximate height" is listed "second"*: *(0.5, 8); (3.5, 6); (6.5, 5); (9.5, 8); (12.5, 3)*. D.) A histogram has a horizontal axis labeled *"Data Value"* from *0 to 16* in *increments of "1"*, and a vertical axis labeled *"Frequency"* from *0 to 10* in *increments of "1"*. The histogram has vertical bars of width 3 starting at the horizontal axis value 0.5. The approximate heights of the bars are as follows, where the *"left horizontal axis label" is listed "first"*, and the *"approximate height" is listed "second"*: *(0.5, 7); (3.5, 5); (6.5, 4); (9.5, 7); (12.5, 2)*. *Part 2:* Create a histogram with *10* classes. Choose the correct histogram below (since I don't have Quizlet+, I can't insert the images of the actual histograms; ergo, I have the descriptions). A.) A histogram has a horizontal axis labeled *"Data Value"* from *0 to 21* in *increments of "1"*, and a vertical axis labeled *"Frequency"* from *0 to 10* in *increments of "1"*. The histogram has vertical bars of width 2 starting at the horizontal axis value 0.5. The approximate heights of the bars are as follows, where the *"left horizontal axis label" is listed "first"*, and the *"approximate height" is listed "second"*: *(0.5, 1); (2.5, 1); (4.5, 4); (6.5, 5); (8.5, 2); (10.5, 4); (12.5, 3); (14.5, 5); (16.5, 0); (18.5, 0)*. B.) A histogram has a horizontal axis labeled *"Data Value"* from *0 to 21* in *increments of "1"*, and a vertical axis labeled *"Frequency"* from *0 to 10* in *increments of "1".* The histogram has vertical bars of width 2 starting at the horizontal axis value 0.5. The approximate heights of the bars are as follows, where the *"left horizontal axis label" is listed "first"*, and the *"approximate height" is listed "second"*: *(0.5, 7); (2.5, 4); (4.5, 6); (6.5, 4); (8.5, 6); (10.5, 6); (12.5, 2); (14.5, 2); (16.5, 1); (18.5, 1)*. C.) A histogram has a horizontal axis labeled *"Data Value"* from *0 to 21* in *increments of "1"*, and a vertical axis labeled *"Frequency"* from *0 to 10* in *increments of "1"*. The histogram has vertical bars of width 2 starting at the horizontal axis value 0.5. The approximate heights of the bars are as follows, where the *"left horizontal axis label" is listed "first"*, and the *"approximate height" is listed "second"*: *(0.5, 5); (2.5, 3); (4.5, 4); (6.5, 2); (8.5, 5); (10.5, 4); (12.5, 1); (14.5, 1); (16.5, 0); (18.5, 0)*. D.) A histogram has a horizontal axis labeled *"Data Value"* from *0 to 21* in *increments of "1"*, and a vertical axis labeled *"Frequency"* from *0 to 10* in *increments of "1"*. The histogram has vertical bars of width 2 starting at the horizontal axis value 0.5. The approximate heights of the bars are as follows, where the *"left horizontal axis label" is listed "first"*, and the *"approximate height" is listed "second"*: *(0.5, 1); (2.5, 2); (4.5, 2); (6.5, 2); (8.5, 3); (10.5, 2); (12.5, 2); (14.5, 1); (16.5, 0); (18.5, 0)*. *Part 3:* Create a histogram with *20* classes. Choose the correct histogram below (since I don't have Quizlet+, I can't insert the images of the actual histograms; ergo, I have the descriptions). A.) A histogram has a horizontal axis labeled *"Data Value"* from *0 to 20* in *increments of "1"*, and a vertical axis labeled *"Frequency"* from *0 to 10* in *increments of "1"*. The histogram has vertical bars of width 1 starting at the horizontal axis value 0.5. The approximate heights of the bars are as follows, where the *"left horizontal axis label" is listed "first"*, and the *"approximate height" is listed "second"*: *(0.5, 1); (1.5, 1); (2.5, 0); (3.5, 1); (4.5, 3); (5.5, 3); (6.5, 2); (7.5, 2); (8.5, 0); (9.5, 3); (10.5, 1); (11.5, 1); (12.5, 2); (13.5, 3); (14.5, 2); (15.5, 0); (16.5, 0); (17.5, 0); (18.5, 0); (19.5, 0)*. B.) A histogram has a horizontal axis labeled *"Data Value"* from *0 to 20* in *increments of "1"*, and a vertical axis labeled *"Frequency"* from *0 to 10* in *increments of "1"*. The histogram has vertical bars of width 1 starting at the horizontal axis value 0.5. The approximate heights of the bars are as follows, where the *"left horizontal axis label" is listed "first"*, and the *"approximate height" is listed "second"*: *(0.5, 2); (1.5, 3); (2.5, 2); (3.5, 1); (4.5, 1); (5.5, 3); (6.5, 0); (7.5, 2); (8.5, 2); (9.5, 3); (10.5, 3); (11.5, 1); (12.5, 0); (13.5, 1); (14.5, 1); (15.5, 0); (16.5, 0); (17.5, 0); (18.5, 0); (19.5, 0)*. C.) A histogram has a horizontal axis labeled *"Data Value"* from *0 to 20* in *increments of "1"*, and a vertical axis labeled *"Frequency"* from *0 to 10* in *increments of "1"*. The histogram has vertical bars of width 1 starting at the horizontal axis value 0.5. The approximate heights of the bars are as follows, where the *"left horizontal axis label" is listed "first"*, and the *"approximate height" is listed "second"*: *(0.5, 3); (1.5, 5); (2.5, 3); (3.5, 1); (4.5, 2); (5.5, 5); (6.5, 0); (7.5, 3); (8.5, 4); (9.5, 4); (10.5, 3); (11.5, 2); (12.5, 2); (13.5, 2); (14.5, 2); (15.5, 0); (16.5, 0); (17.5, 0); (18.5, 0); (19.5, 0)*. D.) A histogram has a horizontal axis labeled *"Data Value"* from *0 to 20 in *increments of "1"*, and a vertical axis labeled *"Frequency"* from *0 to 10* in *increments of "1"*. The histogram has vertical bars of width 1 starting at the horizontal axis value 0.5. The approximate heights of the bars are as follows, where the *"left horizontal axis label" is listed "first"*, and the *"approximate height" is listed "second"*: *(0.5, 0); (1.5, 0); (2.5, 0); (3.5, 1); (4.5, 1); (5.5, 1); (6.5, 1); (7.5, 1); (8.5, 0); (9.5, 2); (10.5, 2); (11.5, 3); (12.5, 3); (13.5, 1); (14.5, 2); (15.5, 1); (16.5, 1); (17.5, 0); (18.5, 0); (19.5, 0)*.
Correct Answers: *Part 1:* D.) A histogram has a horizontal axis labeled *"Data Value"* from *0 to 16* in *increments of "1"*, and a vertical axis labeled *"Frequency"* from *0 to 10* in *increments of "1"*. The histogram has vertical bars of width 3 starting at the horizontal axis value 0.5. The approximate heights of the bars are as follows, where the *"left horizontal axis label" is listed "first"*, and the *"approximate height" is listed "second"*: *(0.5, 7); (3.5, 5); (6.5, 4); (9.5, 7); (12.5, 2)*. *Part 2:* C.) A histogram has a horizontal axis labeled *"Data Value"* from *0 to 21* in *increments of "1"*, and a vertical axis labeled *"Frequency"* from *0 to 10* in *increments of "1"*. The histogram has vertical bars of width 2 starting at the horizontal axis value 0.5. The approximate heights of the bars are as follows, where the *"left horizontal axis label" is listed "first"*, and the *"approximate height" is listed "second"*: *(0.5, 5); (2.5, 3); (4.5, 4); (6.5, 2); (8.5, 5); (10.5, 4); (12.5, 1); (14.5, 1); (16.5, 0); (18.5, 0)*. *Part 3:* B.) A histogram has a horizontal axis labeled *"Data Value"* from *0 to 20* in *increments of "1"*, and a vertical axis labeled *"Frequency"* from *0 to 10* in *increments of "1"*. The histogram has vertical bars of width 1 starting at the horizontal axis value 0.5. The approximate heights of the bars are as follows, where the *"left horizontal axis label" is listed "first"*, and the *"approximate height" is listed "second"*: *(0.5, 2); (1.5, 3); (2.5, 2); (3.5, 1); (4.5, 1); (5.5, 3); (6.5, 0); (7.5, 2); (8.5, 2); (9.5, 3); (10.5, 3); (11.5, 1); (12.5, 0); (13.5, 1); (14.5, 1); (15.5, 0); (16.5, 0); (17.5, 0); (18.5, 0); (19.5, 0)*.
