Statistical Techniques in Business and Economics
Statistical Techniques in Business and Economics
16th Edition
ISBN: 9780077639723
Author: Lind
Publisher: Mcgraw-Hill Course Content Delivery
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Chapter 4, Problem 13E

a.

To determine

Find the first quartile.

Find the third quartile.

a.

Expert Solution
Check Mark

Answer to Problem 13E

The first quartile is 33.25.

The third quartile is 50.25.

Explanation of Solution

Calculation:

Location of percentile:

The formula for percentile is,

LP=(n+1)P100

In the formula, P denotes the location of the percentile and n denotes the total number of observations.

First quartile:

The first quartile represents the 25% of observation lies below first quartile. That is P=25. There are 30 observations in the dataset arranged in ascending order.

Substitute, P=25,n=30 in the percentile formula.

L25=(30+1)25100=31×25100=775100=7.75

The position of first quartile is 7.75th value in the dataset.

First quartile=7thvalue+(8thvalue7thvalue)0.75=31+(3431)0.75=31+2.25=33.25

Hence, the first quartile is 33.25.

Third quartile:

The third quartile represents the 75% of observation lies above third quartile. That is P=75.

Substitute, P=75,n=30 in the percentile formula.

L75=(30+1)75100=31×75100=2,325100=23.25

The position of third quartile is 23.25th value in the dataset.

Third quartile=23rdvalue+(24thvalue23rdvalue)0.25=50+(5150)0.25=50+0.25=50.25

Hence, the third quartile is 50.25.

b.

To determine

Find the second decile.

Find the eighth decile.

b.

Expert Solution
Check Mark

Answer to Problem 13E

The second decile is 27.8.

The eighth decile is 52.6.

Explanation of Solution

Calculation:

Location of decile:

The deciles divide the total observation into 10 equal parts. The formula for decile is,

Di=(n+1)i10

In the formula, i denotes the location of the decile and n denotes the total number of observations.

Second decile:

Substitute, i=2,n=30 in the percentile formula.

D2=(30+1)210=31×210=6210=6.2

The position of second decile is 6.2th value in the dataset.

D2=6thvalue+(7thvalue6thvalue)0.20=27+(3127)0.20=27+0.8=27.8

Hence, the second decile is 27.8.

Eighth decile:

Substitute, i=8,n=30 in the percentile formula.

D8=(30+1)810=31×810=24810=24.8

The position of eighth decile is 24.8th value in the dataset.

D8=24thvalue+(25thvalue24thvalue)0.80=51+(5351)0.80=51+1.6=52.6

Hence, the eighth decile is 52.6.

c.

To determine

Find the 67th percentile.

c.

Expert Solution
Check Mark

Answer to Problem 13E

The 67th percentile is 47.

Explanation of Solution

Calculation:

Substitute, P=67,n=30 in the percentile formula.

L67=(30+1)67100=31×67100=2,077100=20.77

The position of 67th percentile is 20.77th value in the dataset.

67thpercentile=20thvalue+(21thvalue20thvalue)0.77=47+(4747)0.77=47

Hence, the 67th percentile is 47.

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Chapter 4 Solutions

Statistical Techniques in Business and Economics

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