Question

find the mean of the data using the empirical formula when it is given the mode of 50.5 and median is 45.5

Answer 1

We know that 3*median = mode + 2mean
 
 so, 3*45.5 = 50.5+2mean
 so, 2mean = 136.5-50.5
       2mean = 86
       So, Mean = 43

Answer 2

Required Mean = 65.5

Step-by-step explanation:

Given values of Mode and Median of a data are:

Mode = 50.5

Median= 45.5

We have to find the mean of the data using the empirical relation between mean, mode and median.

Since, we know that the empirical formula that relates mean, mode and median is

Mean - Mode = 3 (Mean- Median)

Solving further, we get,

2 Mean = 3 Median - Mode

putting the given values, we get

$\Rightarrow 2 \ Mean = 3\times 45.5 - 50.5\\\Rightarrow Mean = 131 \div 2\\\therefore Mean = 65.5$

So, the required mean of the given data is 65.5.