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 \\( \square \\% \\) of measurements above the 50th percentile and \\( \square \\% \\) of measurements below the 50th 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 is less than or equal to that value.

Step2: Calculate for the 50th percentile

For the \(50\)th percentile (\(p = 50\)):

• The percentage of measurements below the \(50\)th percentile is \(50\%\) (by the definition of percentile).
• The percentage of measurements above the \(50\)th percentile is \(100 - 50=50\%\)

Answer:

There are \(50\%\) of measurements above the \(50\)th percentile and \(50\%\) of measurements below the \(50\)th percentile.