Question

Mina is waiting in line at the Department of Motor Vehicles (DMV). Her wait time of $32$minutes is the ${85}^{th}$ percentile of wait times. Is that good or bad? Write a sentence interpreting the ${85}^{th}$ percentile in the context of this situation.

Short answer

It would be bad for Mina to have to wait time at ${85}^{th}$percentile because $85\%$of people had shorter wait time than Mina and only $15\%$of people had larger wait times than Mina.

Step-by-step solution

Definition

In statistics, the percentiles are the partition values. Percentile divides the entire data into $100$equal parts. The ${50}^{th}$percentiles denotes median and below this value lies $50\%$of data. Similarly ${60}^{th}$percentile will have $60\%$of data below it.

Explanation

The formula for finding the K^th percentile is:

$k^{th}\text{percentile}=\frac{k(N+1)}{100}th\text{item}$

In the given situation, the Mina's waiting time is $32$minutes, which is at ${85}^{th}$percentile value and it would not be good for mina as $85\%$of people had shorter wait time than mina. In this context, mina would prefer a wait time corresponding to a lower percentile. The interpretation of the${85}^{th}$percentile in the given context is$85\%$of people at theDMVwaited$32$minutes or less.