Question

the box plot below represents some data set. what percentage of the data values are greater than 35?

Explanation:

Step1: Recall the properties of a box - plot

In a box - plot, the box is divided into quartiles. The first quartile ($Q_1$) represents the 25th percentile, the median ($Q_2$) represents the 50th percentile, and the third quartile ($Q_3$) represents the 75th percentile. The whiskers extend to the minimum and maximum values.
The value 35 is less than $Q_1$ (the left - hand side of the box).

Step2: Calculate the percentage of data greater than 35

Since 35 is less than $Q_1$, the percentage of data less than $Q_1$ is 25%. Using the formula \(P(\text{data}>x)=100\% - P(\text{data}\leq x)\), we have \(P(\text{data}>35)=100\% - 25\%=75\%\)

Answer:

75%