
Concept explainers
a.
Find the first
Find the third quartile.
a.

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,
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
Substitute,
The position of first quartile is 7.75th value in the dataset.
Hence, the first quartile is 33.25.
Third quartile:
The third quartile represents the 75% of observation lies above third quartile. That is
Substitute,
The position of third quartile is 23.25th value in the dataset.
Hence, the third quartile is 50.25.
b.
Find the second decile.
Find the eighth decile.
b.

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,
In the formula, i denotes the location of the decile and n denotes the total number of observations.
Second decile:
Substitute,
The position of second decile is 6.2th value in the dataset.
Hence, the second decile is 27.8.
Eighth decile:
Substitute,
The position of eighth decile is 24.8th value in the dataset.
Hence, the eighth decile is 52.6.
c.
Find the 67th percentile.
c.

Answer to Problem 13E
The 67th percentile is 47.
Explanation of Solution
Calculation:
Substitute,
The position of 67th percentile is 20.77th value in the dataset.
Hence, the 67th percentile is 47.
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Chapter 4 Solutions
Statistical Techniques in Business and Economics
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