Chapter ISG, Problem 10.1.1P

a.

To determine

To compare samples using median and interquartile range.

Answer to Problem 10.1.1P

Comparison:

  

IQR is interquartile range

Explanation of Solution

Given information:

  

Calculation:

Sample A

Ordered Data

28, 31, 35, 37, 38, 40, 40, 42, 45

n is 9

n is number of frequencies

n is odd

Middle term is 38

Then median is 38

Lower quartile(Q₁)

28, 31, 35, 37

n is 4

n is number of frequencies

n is even

Then middle terms are 31, 35

Then Q₁

  

On solving,

Q₁=33

Upper quartile(Q₂)

40, 40, 42, 45

n is 4

n is number of frequencies

n is even

Middle terms are 40, 42

Then,

  

On solving,

  

Interquartile range=41-33=8

Sample B

Ordered Data

26, 26, 27, 28, 31, 35, 39, 40, 44

n is 9

n is number of frequencies

n is odd

Middle term is 31

Then median is 31

Lower quartile(Q₁)

26, 26, 27, 28

n is 4

n is number of frequencies

n is even

Then middle terms are 26, 27

Then Q₁

  

On solving,

Q₁=26.5

Upper quartile(Q₂)

35, 39, 40, 44

n is 4

n is number of frequencies

n is even

Middle terms are 39, 40

Then,

  

On solving,

  

Interquartile range=39.5-26.5=13

Comparison:

  

IQR is interquartile range

b.

To determine

To explain which sample is more representative.

Answer to Problem 10.1.1P

Sample A gives IQR 8 and sample B gives IQR 13.Sample B having IQR more than Sample A.Then the middle 50% of sample B are spread wide apart.

Explanation of Solution

Given information:

  

Sample A gives IQR 8 and sample B gives IQR 13.Sample B having IQR more than Sample A.Then the middle 50% of sample B are spread wide apart.