Chapter 13.2, Problem 26SR

To determine

To find: Which measure of central tendency best summarizes the test scores.

Answer to Problem 26SR

The central tendency median is best to summarise the test scores.

Explanation of Solution

Given:

  $97,99,95,89,99,100,87,85,89,92,96,95,60,97,85$

Calculation:

The given data is $97,99,95,89,99,100,87,85,89,92,96,95,60,97,85$

Find mean, medina and mode of this data.

  $\begin{array}{c}\text{mean}=\frac{\text{Sum of observations}}{\text{Number of observtions}}\\ =\frac{97+99+95+89+99+100+87+85+89+92+96+95+60+97+85}{15}\\ =\frac{1365}{15}\\ =91\end{array}$

In order to find the median arrange this data in numeric order

  $\text{60, 85, 85, 87, 89, 89, 92, 95, 95, 96, 97, 97, 99, 99, 100}$

The number of data is 15 which is odd.

So, median of the set of the data is the middle value which is $95$

Hence, median is $95$

Now, mode is the number which appears most in the data set.

So, the mode for the given set of data is $\left\{97,99,95,89,85\right\}$

Among the mean, median and mode, the least is mean.

And among mode and median, we can give preference to median.

Therefore, the central tendency median is best to summarise the test scores.