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Chapter 3: Q25 (page 126)

In Exercises 21–28, use the same list of Sprint airport data speeds (Mbps) given for Exercises 17–20. Find the indicated percentile or quartile.

P50

Short Answer

Expert verified

The data speed equal to 1.6 Mbps is in the 50th percentile.

Step by step solution

01

Given information 

The data is recorded for 50 airport data speeds (in Mbps).

02

Method to find observation corresponding to the percentile value

  • For kthpercentile and sample size equal to n, the locator (L) of the data value is calculated using the expression written below:

L=k100×n

  • If the calculated value of L is a whole number, the sum of theLth and the L+1thvalues are obtained from the data when it is arranged in increasing order. The average of two values is the required data value.
  • If the calculated value of L is a decimal number, it is first rounded to the subsequent whole number, and the Lthobservation is the required data value.
03

Computation using the above methods

For k equal to 50 and n equal to 50, the L value is calculated as follows:

L=k100×n=50100×50=25

As L = 25 is a whole number, choose the 25th and the 26th values after arranging the values from the lowest to the greatest.

The corresponding values are 1.6 and 1.6, respectively.

The following computation is done to calculate the data speed (x):

x=25thobs+26thobs2=1.6+1.62=1.6

Therefore,the data speed equal to 1.6 Mbpsis equivalent to the 50th percentile.

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