Question

the boxplot below displays ratings for tv shows during sweeps week. 50% of the shows have a rating greater than: multiple - choice options: 11, 15.5, 14, 17, impossible to tell what is the percentage of shows that have a rating of less than 20?

Explanation:

Step1: Recall box - plot properties

In a box - plot, the box represents the inter - quartile range (IQR), with the lower edge being the first quartile ($Q_1$) and the upper edge being the third quartile ($Q_3$). The line inside the box is the median. The whiskers extend to the minimum and maximum values within a certain range (usually 1.5 * IQR from $Q_1$ and $Q_3$). To find the percentage of data less than a value, we use the properties of quartiles.

Step2: Identify relevant quartile

The median (second quartile, $Q_2$) divides the data into two halves. 50% of the data lies below the median and 50% lies above it. If we want to find the percentage of data less than a value, we note that if the value is greater than the median, more than 50% of the data is less than it. In a box - plot, the median is the middle line of the box.

Step3: Analyze the value 20

Assume the median of the box - plot is at a value less than 20. Since 50% of the data is less than the median, and if 20 is greater than the median, more than 50% of the data is less than 20. Looking at the box - plot, we can see that the median is around 15. Since 20>15, approximately 75% of the data is less than 20.

Answer:

75%