Question

question 10 of 14, step 1 of 1 given the following data, find the percentile of a diameter of 1.41 inches. diameters of golf balls (in inches) 1.68 1.70 1.46 1.33 1.57 1.51 1.45 1.60 1.44 1.30 1.47 1.62 1.56 1.70 1.64 1.56 1.67 1.56 1.49 1.49

Explanation:

Step1: Sort the data

Sort the given data set of golf - ball diameters in ascending order: 1.30, 1.33, 1.44, 1.45, 1.46, 1.47, 1.49, 1.49, 1.51, 1.56, 1.56, 1.56, 1.57, 1.60, 1.62, 1.64, 1.67, 1.68, 1.70, 1.70.

Step2: Use the percentile formula

The formula for the percentile \(P\) of a value \(x\) in a data - set of size \(n\) is \(L=\frac{k}{100}(n + 1)\), where \(k\) is the percentile we want to find and \(n\) is the number of data points. Here, \(n = 20\).
We want to find the percentile of \(x = 1.41\). First, count the number of values less than 1.41. There are 0 values less than 1.41.
The formula for the percentile rank \(PR=\frac{\text{number of values less than }x}{n}\times100\).
Substitute the values: \(\text{number of values less than }1.41 = 0\) and \(n = 20\) into the formula.
\(PR=\frac{0}{20}\times100 = 0\).

Answer:

0