Chapter 11.6, Problem 23PPSE

Solution

Toidentify:The student’s error if he claims89 is at the 70^th percentile if the set of values is 1, 1, 1, 1, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 89, 89, 89, 89, 89

Left most 89 is at 75^th percentile. Rest 89s will have greater percentile.

Given information:

The set of values is 1, 1, 1, 1, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 89, 89, 89, 89, 89

Explanation:

Consider the given information.

The given data set is in ascending order.

The given data set is in ascending order.

Let us consider the left most 89. Left most 89 is at the 15^th position. Total number of data values in the data set is 20.

  $\begin{array}{c}20\times percentile=15\\ percentile=\frac{15}{20}\\ =0.75\end{array}$

Hence, left most 89 is at 75^th percentile. Rest 89s will have greater percentile.