Arithmetic

Central Tendency

Medium

In a moderately asymmetrical distribution, the mode and mean are 31.5 and 34.5, respectively. Calculate the median:

100.5

25.5

33.5

27.5

✅ Correct Option: 3

Given:

Mode $= 31.5$

Mean $= 34.5$

For a moderately asymmetrical distribution, the relationship between mean, median, and mode is:

Mean $-$ Mode $= 3$ (Mean $-$ Median)

This is Karl Pearson's empirical relationship for moderately skewed distributions.

Substituting the given values:

$34.5 - 31.5 = 3(34.5 - \text{Median})$

$3 = 3(34.5 - \text{Median})$

Dividing by $3$ :

$1 = 34.5 - \text{Median}$

$\text{Median} = 34.5 - 1$

$\text{Median} = 33.5$

2022: 8 Aug Shift 1

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2022: 24 Aug Shift 1

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Read the information given below carefully and answer the question that follows:

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Choose the correct answer from the options given below:

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Match List I with List II

List I	List II
Statistical Measure	Definition
(A) Mode	(I) Sum of all observations divided by their count
(B) Median	(II) Measure of the spread from the mean
(C) Mean	(III) Central value when observations are arranged in order
(D) Standard Deviation	(IV) Observation which has the highest frequency

Choose the correct answer from the options given below:

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In a moderately asymmetrical distribution, the mode and mean are 31.5 and 34.5, respectively. Calculate the median:

Solution

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