Question

On a $60$point written assignment, the $80th$percentile for the number of points earned was $49$. Interpret the $80th$percentile in the context of this situation.

Short answer

It's worth noting that the percentile doesn't always equal the value of an observation because it's calculated using sample data. As a result, the percentile may not correspond to any of the data points. The $80th$percentile is $49$, thus the data below is $80$percent and the data above is $20$percent.

Step-by-step solution

Introduction

On a scale of $60$, the $80th$percentile signifies that the number above it represents 20 % observation and the number below it represents $80\%$observation.

Explanation

We split the population into $100$sub-parts, and the above to percentile value is $100*(1-p)\%$observation, while the below to percentile value is $100*p\%$observation. where $0$is the starting point