Concept explainers
(a)
Antawn’s percentile having head circumference of 22.4 inches.
(a)
Answer to Problem 3E
Percentile that corresponds with head circumference of 22.4 inches is 33rd percentile.
Explanation of Solution
Given information:
Measurements of head circumference (in inches):
Let
n , Number of data values that are less than the individual’s data value
N , Total number of data values
Now,
Sort all the data values in ascending order:
20.8, 20.8, 21.0, 21.5, 21.6, 21.7, 21.9, 22.0, 22.2, 22.3, 22.4, 22.5, 22.5, 22.6, 22.6, 22.7, 22.7, 22.7, 23.0, 23.0, 23.1, 23.3, 23.4, 23.5, 23.5, 23.9, 23.9, 24.0, 24.2, 25.6.
Note that
10 of the 30 data values are smaller than 22.4.
Percentile can be determined as the number of data values that are less than the individual’s data value ( n ), divided by the total number of data values ( N ), written as percentage.
Thus,
Percentile that corresponds with head circumference of 22.4 inches is 33rd percentile.
(b)
Head circumference of the player at the 90th percentile of the distribution.
(b)
Answer to Problem 3E
Head circumference at the 90thpercentile is 24.0 inches.
Explanation of Solution
Given information:
Measurements of head circumference (in inches):
Let
n , Number of data values that are less than the individual’s data value
N , Total number of data values
Now,
Sort all the data values in ascending order:
20.8, 20.8, 21.0, 21.5, 21.6, 21.7, 21.9, 22.0, 22.2, 22.3, 22.4, 22.5, 22.5, 22.6, 22.6, 22.7, 22.7, 22.7, 23.0, 23.0, 23.1, 23.3, 23.4, 23.5, 23.5, 23.9, 23.9, 24.0, 24.2, 25.6.
Note that
The data set consists of 30 data values.
Such that
The data value represented by the xth percentile has x% of the data values below it.
Then
90th percentile has 90% of the 30 data values below it.
Calculate 90% of 30 data values:
We have
27 out of 30 data values are smaller than 90th percentile.
90th percentile needs to be the 28th data value in the ascending order, and that is 24.0.
Thus,
Head circumference of the player at the 90thpercentile of the distribution is 24.0 inches.
Chapter 2 Solutions
PRACTICE OF STATISTICS F/AP EXAM
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