Chapter 13, Problem 6CT

To determine

To find the mean, median and mode(s) of the data set 3, 10, 5, 12, 6, 7, 5.

Answer to Problem 6CT

Mean = 6.857, Median = 6 and Mode = 5

Explanation of Solution

Given information :

The data set given is: 3, 10, 5, 12, 6, 7, 5

Concept used:

1.Mean of n numbers is equal to $\frac{\text{the sum of the numbers}}{n}$ .

2.The median of n numbers:

• When n is odd, the middle number, that is., $\frac{n+1}{2}\text{th}$ term, when the numbers arewritten in order, will be the median.
• When n is even, the median is the average of the two middle numbers. The two middle numbers will be, $\frac{n}{2}$ th and $\frac{n+2}{2}$ th term and there average will be: $\frac{\frac{n}{2}+\frac{n+1}{2}}{2}=\frac{2n+1}{4}$ .

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

• When twonumbers occur most frequently for the same number of times, then the collection has two modes and is calledbimodal.
• When no number occurs more than once, the data set has no mode.

Calculations:

Mean = $\frac{3+10+5+12+6+7+5}{7}=\frac{48}{7}=6.857$

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

Data set arranged in increasing order: 3, 5, 5, 6, 7, 10, 12.

Since the number of terms are 7, therefore the median will be the middle term, that is., $\frac{7+1}{2}=\frac{8}{2}=4\text{th}$ term and the 4^th term is 6.

Hence, median = 6.

For mode, observe which number is occurring more frequently. Clearly, 5 is the only number which appeared twice. Therefore, mode = 5.