Question

Find the median of the dtata, using an empirical relation when it is given that mode =12.4 and mean=10.5

Answer 1

Tip:

Recall the concept of mean, median, and mode

The arithmetic mean is calculated by adding the numbers and dividing the sum by the number of numbers in the list.

The median is the middle value in a list ordered in ascending or descending order.

The mode is the most frequently occurring value on the list.

The empirical relation of mean median and mode is $mode=3median-2mean$

Given:

Mode$=12.4$, Mean$=10.5$

Explanation:

The formula is $mode=3median-2mean$

$\implies 12.4=3median-2(10.5)$

$\implies 12.4=3median-21$

$\implies 3median=12.4+2(10.5)$

$\implies 3median=33.4$

$\implies median=\frac{33.4}{3}$

$\implies median=11.13$

Hence the median is $11.13$

Answer 2

Given,

Mode =12.4 and Mean=10.5

To Find,

The median =?

Solution,

We can solve the question as follows:

It is given that the mode and the mean of a given set of data are 12.4 and 10.5 respectively. We have to use an empirical relation and find the median.

$Mode = 12.4$

$Mean = 10.5$

The relation between mean, mode, and the median is given as:

$3Median = Mode + 2Mean$

Substituting the values in the above formula,

$3Median = 12.4 + 2*10.5$

$3Median = 12.4 + 21$

$3Median = 33.4$

$Median = \frac{33.4}{3} = 11.13$

Hence, the median is equal to 11.13.