Question

a speed camera recorded the speeds of 100 cars in miles per hour. the box - plot below shows the results. the median speed recorded was 45 miles per hour. what percentage of the cars were going from 40 to 45 miles per hour?

Explanation:

Step1: Recall box - and - whisker plot properties

In a box - and - whisker plot, the box represents the inter - quartile range (IQR), which contains 50% of the data. The median divides the data set into two halves. If we assume the box spans from the first quartile ($Q_1$) to the third quartile ($Q_3$), and we want to find the percentage of data in a certain range related to the median.

Step2: Analyze the range

We know that the median is 45 miles per hour. The range is from 40 to 45 miles per hour. If we consider the properties of a box - and - whisker plot, and assume the data is symmetrically distributed around the median (a reasonable assumption for a well - behaved data set), and since the box contains 50% of the data and is centered around the median. The range from 40 to 45 is half of the inter - quartile range (assuming a symmetric distribution around the median). So the percentage of cars going from 40 to 45 miles per hour is 25%.

Answer:

25%