Question

The mode is 15.find mean and median using empirical relation.

CI-1 5 9 13 17
Fi-7 2 2 8 1 ​

Answer 1

Given:

The mode is 15.

CI-1 5 9 13 17

Fi-7 2 2 8 1

To find:

Find mean and median using empirical relation.

Solution:

From given, we have,

x       f            x × f

1       7              7

5      2              10

9      2              18

13     8              104

17     1               17

     ∑f = 20     ∑x × f = 156

Mean = ∑x × f / ∑f  = 156/20

∴ Mean = 7.8

∴ Mode = 15             (∵ given)

The empirical relationship between mean, median and mode is given as follows,

Mean - Mode = 3(Mean - Median)

7.8 - 15 = 3(7.8 - Median)

-7.2 = 3(7.8 - Median)

-2.4 = 7.8 - Median

Median = 7.8 + 2.4

∴ Median = 10.2