Chapter 13, Problem 7CT

To determine

To find the mean, median and mode(s) of the data set 25, 39, 36, 43, 37, 36.

Answer to Problem 7CT

Mean = 36, Median = 36, 37 and Mode = 36

Explanation of Solution

Given information :

The data set given is: 25, 39, 36, 43, 37, 36

Concept used:

1. The mean of n numbers is the sum of the numbers divided by n .

2.The median of n numbers is the middle number when the numbers are

written in order. When n is even, the median is the average of the two middle numbers.

3. The mode of n numbers is the number that occurs most frequently. When two

numbers tie for most frequent occurrence, the collection has two modes and is called

bimodal. When no entry occurs more than once, the data set has no mode.

Calculations:

Mean = $\frac{25+39+36+43+37+36}{6}=\frac{216}{6}=36$

In order to calculate median, arrange the data set in order (either increasing or decreasing):

Data set arranged in increasing order: 25, 36, 36, 37, 39, 43.

Since the number of terms are 6, which is even, therefore, there will be two middle terms, that is., 36 and 37, and both will be the medians.

Hence, median = 36 and 37.

For mode, observe which number is occurring more frequently. Clearly, 36 is the only number which appeared twice. Therefore, mode = 36.