Question

give the percentage of measurements in a data set that are above and below each of the following percentiles.
a. 55th percentile b. 50th percentile
c. 30th percentile d. 84th percentile
a. there are 45 % of measurements above the 55th percentile and 55 % of measurements below the 55th percentile. (simplify your answers.)
b. there are 50 % of measurements above the 50th percentile and 50 % of measurements below the 50th percentile. (simplify your answers.)
c. there are 70 % of measurements above the 30th percentile and 30 % of measurements below the 30th percentile. (simplify your answers.)
d. there are % of measurements above the 84th percentile and % of measurements below the 84th percentile. (simplify your answers )

Explanation:

Step1: Recall percentile concept

A $p$ -th percentile divides a data - set such that $p\%$ of the data is below it and $(100 - p)\%$ is above it.

Step2: Calculate for 84th percentile

For the 84th percentile, the percentage of measurements below is 84% and the percentage of measurements above is $100 - 84=16\%$.

Answer:

There are 16% of measurements above the 84th percentile and 84% of measurements below the 84th percentile.