Q 91. - The Practice of Statistics for AP

Question

Don’t call me In a September $28, 2008$, article titled “Letting Our Fingers Do the Talking,” the New York Times reported that Americans now send more text messages than they make phone calls. According to a study by Nielsen Mobile, “Teenagers ages $13$ to $17$ are by far the most prolific texters, sending or receiving $1,742$ 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 and calls they had sent or received in the past $24$ hours. Here are the texting data:

(a) Make a boxplot of these data by hand. Be sure to check for outliers.

(b) Do these data support the claim in the article about the number of texts sent by teens? Justify your answer with appropriate evidence.

Step-by-Step Solution

Answer

Part (b) No

Part (a) 

Part (a) Step 1: Given information

Given data : 

0	7	1	29	25	8	5	1	25	98	9	0	26
8	118	72	0	92	52	14	3	3	44	5	42

Part (a) Step 2: Concept

A boxplot is a frequent data analysis graph.

Part (a) Step 3: Calculation

The following is a box plot of data from first-period statistics class on the number of text messages and phone calls they sent or received in the previous $24$ hours: 

To look for outliers, we'll first calculate the IQR and then determine the upper and lower limits: $$\begin{gathered} IQR = {Q }_3- Q_1 \\ = 43 - 3 \\ = 40 \\ IQRx1.5 = 40x1.5 \\ = 60 \\ { Q}_3 + 60 = 43 + 60 \\ = 103 \\ {Q}_1- 60 = 3 - 60 \\ = -57 \end{gathered}$$

An outlier is a figure that is greater than $103$ but less than $-57$, in this example $118$ Thus, a box plot is made for the given data.

Part (b) Step 1: Calculation

Within $24$ hours, four of the $25$ students in the data set sent at least $58$ texts. The data contradicts the conclusions, as the majority of teenagers send an average of $9$ texts each day, resulting in $9 x 30 = 270$ texts per month, which is far less than the findings.