Question

The empirical relationship among the three measures of central tendencies is
1. 2 Median = Mode + Mean
2. 3 Median = Mode + 2 Mean
3. Median = Mode + Mean
4. Median = 2 Mode + 3 Mean

Answer 1

Correct Answer - Option 2 : 3 Median = Mode + 2 Mean

Concept

The relationship between mean, median and mode is called empirical relationship. It is defines as :

Mean - Mode = 3(Mean - Median)

Calculation

Mean - Mode = 3(Mean - Median)

⇒ Mean - Mode = 3 Mean - 3 Median

⇒ 3 Median - Mode = 3 Mean - Mean

⇒ 3 Median = 2 Mean + Mode

∴ 3 Median = Mode + 2 Mean