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Which of the following relationships is true in a modal distribution?
Question



Which of the following relationships is true in a modal distribution?

A.

Mean – Mode = 3 (Mean – Median)

B.

Mode = 3 Median – 2 Mean

C.

3 Median = 2 Mean - Mode

D.

2 Median – 3 Quartile Deviation = Mean

Correct option is B

In a modal distribution, the relationship between the mean, median, and mode is typically represented by the empirical rule, which states:
· Mode = 3 Median – 2 Mean. This formula is often used in the context of symmetric and unimodal distributions, particularly in cases where the distribution is approximately normal or skewed. It gives an approximate relationship between the three central measures.
Information Booster:
· The empirical relationship helps estimate the mode if the median and mean are known.
· This formula assumes a roughly symmetric distribution, where the mean, median, and mode are related in a specific way.
· It is mostly applicable to unimodal distributions where a single peak dominates.
· When the distribution is skewed, this rule may not hold perfectly.
· Median is the middle value, Mode is the most frequent value, and Mean is the arithmetic average.

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