Question

give the percentage of measurements in a data set that are above and below each of the following percentiles.
a. 85th percentile b. 50th percentile
c. 30th percentile d. 64th percentile
a. there are 15% of measurements above the 85th percentile and 85% of measurements below the 85th 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 64th percentile and % of measurements below the 64th percentile. (simplify your answers.)

Explanation:

Step1: Recall the definition of percentile

The \(p\)th percentile of a data set is a value such that \(p\%\) of the data values are less than or equal to this value.

Step2: Calculate for the 64th percentile

For the percentage of measurements below the 64th percentile, by the definition of percentile, it is \(64\%\).
For the percentage of measurements above the 64th percentile, we use the formula \(100 - p\). Here \(p = 64\), so \(100-64=36\%\)

Answer:

There are \(36\%\) of measurements above the 64th percentile and \(64\%\) of measurements below the 64th percentile.