Question

In a survey collecting data about the salaries earned by recent college graduates, Li found that her salary was in the ${78}^{th}$percentile. Should Li be pleased or upset by this result? Explain

Short answer

Li should be pleased with her salary.

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 denote 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, Li's salary is at ${78}^{th}$percentile; which means$78\%$of recent college graduates earn less than Li does.$22\%$of recent college graduates earn more than Li does.