Question

the box - and - whisker plot below represents some data set. what percentage of the data values are greater than or equal to 83?

Explanation:

Step1: Recall box - and - whisker plot percentiles

In a box - and - whisker plot, the data is divided into four quartiles. The median (second quartile, \(Q_2\)) divides the data into two halves, each containing 50% of the data. The first quartile (\(Q_1\)) divides the lower half into two parts (25% each), and the third quartile (\(Q_3\)) divides the upper half into two parts (25% each). So, the data is split such that 25% of the data is below \(Q_1\), 25% is between \(Q_1\) and \(Q_2\), 25% is between \(Q_2\) and \(Q_3\), and 25% is above \(Q_3\). Also, the median (\(Q_2\)) is the middle value, and 50% of the data is above the median, 50% is below.

Looking at the box - and - whisker plot, the value 83 is the median (since the line inside the box is at 83, which represents the median or \(Q_2\)).

Step2: Determine the percentage of data greater than or equal to the median

Since the median (\(Q_2\)) divides the data into two equal parts, 50% of the data is greater than or equal to the median (and 50% is less than or equal to the median). So, if 83 is the median, the percentage of data values greater than or equal to 83 is 50%.

Answer:

50%