Question

Mean of a data set is 22. if the ratio of the mode and median of the data set is 1 : 3, the find the correct relation between mean, median and mode.
1. Mean > Median > Mode
2. Mode > Median > Mean
3. Median = Mode > Mean
4. Mean = Mode < Median

Answer 1

Correct Answer - Option 1 : Mean > Median > Mode

Given;

Mean of a data set = 22

Ratio of Mode and Median = 1 : 3

Formula Used:

Mode = 3(Median) - 2(Mean)

Calculation:

Ratio of mode and Median be 1x : 3x

x = 3 × (3x) - (2 × 22)

⇒ 8x = 44

⇒ x = 44/8

⇒ x = 5.5

Since Mode is x so Mode of the data is 5.5

Median = 3x = 3 × 5.5

Median = 16.5

Mean = 22

Mode = 5.5

∴ The Correct relation is Mean > Median > Mode