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

P60

Short Answer

Expert verified

The data speed corresponding to the 60th percentile is 2.45 Mbps.

Step by step solution

01

Given information 

The data given contains a set of 50 airport data speeds (in Mbps).

02

Steps to obtain the value corresponding to the given percentile 

The percentileof a value indicates the location of the value relative to all the other observations.

The data value corresponding to a given percentile is calculated in the following steps:

  • Compute L=k100n.

Here, L is the locator of the value;

k is the percentile of the value;

n is the total number of values.

  • If L turns out to be a whole number, compute the average of the Lthobservation and theL+1th observation from the sorted data. This average is treated as the data value corresponding to the given percentile.
  • If L contains decimals, the value of L is rounded to the next whole number.
  • Now, the Lthvalue is the data value corresponding to the given percentile.
03

Step 3: Follow the steps to find the value corresponding to the 60th percentile

Sort the values from the smallest to the largest, andenumerate the total number of observations.

L=k100n=6010050=30

As L =30 is a whole number, locate the 30th and the 31st observation from the sorted data, and divide their sum by 2, which is 2.4 and 2.5, respectively.

The data value (x) is computed as follows:

x=30thobs+31stobs2=2.4+2.52=2.45

Therefore,the data speed corresponding to the 60th percentile is 2.45 Mbps.

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