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For the data set, find the median, the first and third quartiles ..., Lecture notes of Statistics

Colorado Christian University (CCU)Statistics

ANSWER: ranges: 50 and 45; medians: both 50; Q1: 45 and 35; Q3: both 60; IQR: 15 and 25; Sample answer: Both sets of data have the same median number of minutes ...

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Forthedataset,findthemedian,thefirstandthirdquartiles,andtheinterquartilerange.

2.textsperday:24,53,38,12,31,19,26

SOLUTION:

Orderthenumbersfromleasttogreatest.

12,19,24,26,31,38,53

Themiddlevalueis26.Thefirstquartileis19.Thethirdquartileis38.

Thedifferencebetweenthefirstandthirdquartileis19.

ANSWER:

median:26;Q1:19;Q3:38;IQR:19

4.Thetableshowsthenumberofminutesofexerciseforeachperson.Compareandcontrastthemeasuresofvariation

forbothweeks.



SOLUTION:

TherangeforWeek1is90–40or50.TherangeforWeek2is75–30or45.

Orderthenumbersforthefirstweekfromleasttogreatest:40,45,45,55,60,90

Orderthenumbersforthesecondweekfromleasttogreatest:30,35,45,55,60,75



Themedianofthefirstweekis or50.

Themedianofthesecondweekis or50.



Thefirstquartileofthefirstweekis45.Thefirstquartileofthesecondweekis35.



Thethirdquartileofthesecondweekis60.Thethirdquartileofthesecondweekis60.



Sampleanswer:Bothsetsofdatahavethesamemediannumberofminuteswhilethemiddledatainthefirstsetare

groupedmorecloselythanthemiddledatainthesecond.

ANSWER:

ranges:50and45;medians:both50;Q1:45and35;Q3:both60;IQR:15and25;Sampleanswer:Bothsetsofdata

havethesamemediannumberofminuteswhilethemiddledatainthefirstsetaregroupedmorecloselythanthe

middledatainthesecond.

eSolutions Manual - Powered by Cognero Page 1

11-3MeasuresofVariation

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Download For the data set, find the median, the first and third quartiles ... and more Lecture notes Statistics in PDF only on Docsity!

For the data set, find the median, the first and third quartiles, and the interquartile range.

texts per day: 24, 53, 38, 12, 31, 19, 26 SOLUTION: Order the numbers from least to greatest. 12, 19, 24, 26, 31, 38, 53 The middle value is 26. The first quartile is 19. The third quartile is 38. The difference between the first and third quartile is 19. ANSWER: median: 26; Q 1 : 19; Q 3 : 38; IQR: 19
The table shows the number of minutes of exercise for each person. Compare and contrast the measures of variation for both weeks. SOLUTION: The range for Week 1 is 90 – 40 or 50. The range for Week 2 is 75 – 30 or 45. Order the numbers for the first week from least to greatest: 40, 45, 45, 55, 60, 90 Order the numbers for the second week from least to greatest: 30, 35, 45, 55, 60, 75 The median of the first week is or 50. The median of the second week is or 50. The first quartile of the first week is 45. The first quartile of the second week is 35. The third quartile of the second week is 60. The third quartile of the second week is 60. Sample answer: Both sets of data have the same median number of minutes while the middle data in the first set are grouped more closely than the middle data in the second. ANSWER: ranges: 50 and 45; medians: both 50; Q 1 : 45 and 35; Q 3 : both 60; IQR: 15 and 25; Sample answer: Both sets of data have the same median number of minutes while the middle data in the first set are grouped more closely than the middle data in the second.

Use Math Tools The double stem-and-leaf plot, where the stem is in the middle and the leaves are on either side, shows the high temperatures for two cities in the same week. Use the measures of variation to describe the data in the stem-and-leaf plot. SOLUTION: Minneapolis Order the numbers from least to greatest: 20, 21, 23, 25, 34, 36, 43 The range is 43 – 20 or 23. The median is 25, the first quartile is 21, and the third quartile is 36. The interquartile range is 36 – 21 or 15. Columbus Order the numbers from least to greatest: 25, 27, 29, 29, 37, 48, 62 The range is 62 – 25 or 37. The median is 29, the first quartile is 27, and the third quartile is 48. The interquartile range is 48 – 27 or 21. Sample answer: The Minneapolis temperatures are closer together than the Columbus temperatures. ANSWER: Minneapolis—range: 23; degrees; Q 3 : 36 degrees; Q 1 : 21 degrees; IQR: 15 degrees; Columbus—range: 37 degrees; Q 3 : 48 degrees; Q 1 : 27 degrees; IQR: 21 degrees; Sample answer: The Minneapolis temperatures are closer together than the Columbus temperatures.
Reason Abstractly Create a list of data with at least six numbers that has an interquartile range of 15 and two outliers. SOLUTION: Sample answer: 6, 30, 33, 41, 45, 71 The first quartile is 30, the third quartile is 45. The interquartile is 45 – 30 or 15. The two outliers are 6 and 71. ANSWER: Sample answer: 6, 30, 33, 41, 45, 71

Find the median, the first and third quartiles, and the interquartile range for the cost of admission: $13.95, $24.59, $19.99, $29.98, $23.95, $28.99. SOLUTION: Order the numbers from least to greatest. $13.95, $19.99, $23.95, $24.59, $28.99, $29. The median is or $24.27. The first quartile is $19.99 and the third quartile is $28.99. The interquartile range is 28.99 – 19.99 or $9.00. ANSWER: median: $24.27; Q 1 : $19.99; Q 3 : $28.99; IQR: $9.
The data shows the number of dogs enrolled in different obedience classes. a. Order the values from least to greatest. b. Find the range of the data. c. Find the median and the first and third quartiles. d. Find the interquartile range. SOLUTION: Order the numbers from least to greatest: 6, 8, 9, 10, 10, 12, 12, 15, 20, 22 The range is 22 – 6 or 16. The median is 11. The first quartile is 9. The third quartile is 15. The interquartile range is 15 – 9 or 6. ANSWER: a. 6, 8, 9, 10, 10, 12, 12, 15, 20, 22 b. 16 c. 11, 9, 15 d. 6

Divide.

188 ÷ 8 SOLUTION: ANSWER:

22. 74.4 ÷ 6

SOLUTION:

ANSWER:

Refer to the table. How many more hours did Koli work in week 2 than in week 3? SOLUTION: Koli worked 16 – 9 or 7 more hours in week 2 than in week 3. ANSWER: 7 hours