Question

A.Find the mean, median, and mode of 14, 15, 3, 15, 14, 14, 18, 15, 8, 16

Answer 1

Given:

The data set is:

14, 15, 3, 15, 14, 14, 18, 15, 8, 16

To find:

The mean, median and mode of the given data set.

Solution:

We have,

14, 15, 3, 15, 14, 14, 18, 15, 8, 16

Arrange the data values in ascending order.

3, 8, 14, 14, 14, 15, 15, 15, 16, 18

Mean of the data set is:

`Mean=\frac{\text{Sum of all observations}}{\text{Number of observation}}`

`Mean=(3+8+14+14+14+15+15+15+16+18)/(10)`

`Mean=(132)/(10)`

`Mean=13.2`

The number of observation is 10 which is an even number. So, the median of the data set is:

`Median=\frac{((n)/(2))\text{th term}+((n)/(2)+1)\text{th term}}{2}`

`Median=\frac{((10)/(2))\text{th term}+((10)/(2)+1)\text{th term}}{2}`

`Median=\frac{5\text{th term}+6\text{th term}}{2}`

`Median=(14+15)/(2)`

`Median=(29)/(2)`

`Median=14.5`

Mode is the most frequent value of the data set.

In the given data set the highest frequency is 3 because 14 and 15 occurs three times.

So, the mode of the given data set is 14 and`15.

Therefore, the mean is 13.2, median is 14.5 and mode is 14 and 15.