Don’t call meAccording to a study by Nielsen Mobile, “Teenagers ages 13 to 17 are by far the most prolific texters, sending 1742 messages a month.” Mr. Williams, a high school statistics teacher, was skeptical about the claims in the article. So he collected data from his first-period statistics class on the number of text messages they had sent in the past 24 hours. Here are the data:

(a) Make a boxplot of these data.

(b) Use the boxplot you created in part (a) to explain how these data seem to contradict the claim in the article.

The given data in the sorted form is:

0, 0, 0, 1, 1, 3, 3, 5, 5, 8, 8, 9, 14, 25, 25, 26, 29, 42, 44, 52, 72, 92, 98, 118

As the number of data, values is odd, and the median is 9.

The median of data values below the median (or at 25% of the data) is the first quartile. The first quartile is the average of the 6th and 7th data values because there are 12 data values below the median.

$$\begin{gathered} Q_1=\frac{3+3}{2} \\ =3 \end{gathered}$$

The median of the data values above the median (or at 75% of the data) is the third quartile. The third quartile is the average of the 18th and 19th data values since there are 12 data values above the median.

$$\begin{gathered} Q_3=\frac{42+44}{2} \\ =43 \\ IQR=43-3 \\ =40 \end{gathered}$$

Observations that are more than 1.5 times the IQR above the third quarter or below the first quarter are considered outliers.

$$\begin{gathered} Q_3+1.5IQR=43+1.5\left(40\right) \\ =103 \\ {Q}_1-1.5IQR=3-1.5\left(40\right) \\ =-57 \end{gathered}$$

From the data, we know that 118 is an outlier.

An Xis used to represent outliers. The boxplot's whiskers are at the minimum and highest values. The box has a vertical line at the median and starts at the first quartile and finishes at the third quartile.

Teens send 1742 texts every month, or approximately 58 texts every 24 hours, according to the claim.

Only four of the twenty-five students sent at least 58 texts in a 24-hour period, according to the data.

As a result, it indicates that the assertion is false, as most students send far fewer than 58 messages in a 24-hour period.