Q. 7 - The Practice of Statistics for AP

Question

Forty students took a statistics examination having a maximum of 50 points. The score distribution is given in the following stem-and-leaf plot:

The third quartile of the score distribution is equal to (a) 45. (b) 44. (c) 43. (d) 32. (e) 23.

Step-by-Step Solution

Answer

The score distribution's third quartile is 44 i.e option (b)

Step 1: Given information

Given,

Step 2: Explanation for correct option

The third quartile position will be determined as follows:

$\begin{array}{rcl}{Q}_3& =& \frac{3\times 40}{4}\\ & =& {30}^{\text{th }}\end{array}$

The third quartile, or the ${30}^{\text{th }}$ score of the score distribution, is equal to 44, according to the score distribution stem plot.

Hence, option (b) is correct

As a result, the score distribution's third quartile is 44.

Step 3: Explanation for incorrect option

(a) The third quartile of the score distribution will not be equal to $45$.

(c) The third quartile of the score distribution will not be equal to $43$.

(d) The third quartile of the score distribution will not be equal to $32$.

(e) The third quartile of the score distribution will not be equal to $23$.