Question

Mean, Median and Mode of a data are related by the relation

• A. 3 Mode - 2 Median = Mean
• B. 3 Mean - 2 Mode = Median
• C. 3 Median - 2 Mode = Mean
• D. 3 Median - 2 Mean = Mode

Answer 1

The Correct Option is D

The relationship between the mean, median, and mode in a skewed distribution is an important aspect of descriptive statistics. The specific formula that relates these three measures of central tendency is known as the "Empirical Relationship" or sometimes called the "Empirical Rule" for skewed distributions. For skewed data:

The formula is: 3 Median - 2 Mean = Mode

Explanation:

• Mean is the arithmetic average of a data set and is sensitive to extremely high or low values.
• Median is the middle value of the data when arranged in order. It is often a better measure of central tendency for skewed distributions because it is not affected by outliers.
• Mode is the value that appears most frequently in the data set.

In skewed distributions, the mean is pulled towards the tail, and the relationship: 3 Median - 2 Mean = Mode can be derived based on empirical observations in many types of skewed data.