Chapter 10.1, Problem 11IP

To determine

To find: the appropriate measure of centre.

Answer to Problem 11IP

Median is the most appropriate measure which can be used to describe the test score.

Explanation of Solution

Given information:

The dataset of math test scores for which appropriate measure of centre needs to be determine is as follows

  $80,76,94,90,88,92,88,96$ ..

Formula used:

1) $\text{mean=}\frac{\text{Sum}\text{of}\text{the}\text{data}}{\text{number}\text{of}\text{items}\text{in}\text{data}\text{set}}$

2) median= middle number of data arranged from least to greatest.

3) mode = number or data occurred most often.

Calculation:

Test scores are as follows

  $80,76,94,90,88,92,88,96$

Calculate mean of dataset

Mean = $\frac{80+76+94+90+88+92+88+96}{8}$

  $=\frac{704}{8}$

  $=88$

Calculate median of dataset

Arrange the math test score in ascending order.

  $76,80,88,88,90,92,94,96$

Since number of math test score is even that is 8 so median is

  $\left(\frac{4^{th}term+5^{th}term}{2}\right)$

Median = $\frac{88+90}{2}$

= $\frac{178}{2}$

= $89$

Calculate mode of dataset

Arrange the math test score in ascending order.

  $76,80,88,88,90,92,94,96$

Mode = $88$

Median that is 89 is the greatest value of the three measures. Since M wants to show a high test score, so median is the appropriate measure.