Question

Forty students took a statistics test worth 50 points. The dotplot displays the data. The third quartile is

a. 45.

b. 32.

c. 44.

d. 23.

e. 43.

Short answer

The correct option is (b)

b 44

Step-by-step solution

Step 1. Given information.

a. 45.

b. 32.

c. 44.

d. 23.

e. 43.

Step 2.  The best option.

Let us first determine all data values from the dotplot, where data values are the horizontal axis values that correspond with the dots in the dotplot.

2, 8, 12, 12, 14, 15, 20, 21, 23, 23, 23, 23, 25, 28, 28, 28, 29, 30, 30, 31, 33, 35, 36, 36, 37, 39, 42, 42, 44, 44, 44, 44, 46, 46, 47, 48, 48, 50, 50, 50

The data values in the dotplot were already ordered.

The median is the sorted data set's middle value. Because the number of data values is even, the median is the average of the sorted data set's two middle values (20th and 21st data values).

$$\begin{gathered} M=Q_2=\frac{31+33}{2} \\ \frac{31+33}{2}=\frac{64}{2} \\ \frac{64}{2}=32 \end{gathered}$$

The third quartile is the median of the data values that are greater than the median (or at 75 percent of the data). The third quartile is the average of the 30th and 31st data values because there are 20 data values above the

$$\begin{gathered} Q_3=\frac{44+44}{2} \\ \frac{44+44}{2}=\frac{88}{2} \\ \frac{88}{2}=44 \end{gathered}$$

As a result:

(b) 44