The mean of a distribution is 72, and the mean exceeds the mode by 12. In this distribution, the value (Mean - Median) is one-third of (Mean - Mode). Find the median.
68
Mean = 72 and Mean − Mode = 12, so Mode = 72 − 12 = 60.
Mean − Median = \(\frac{1}{3}\) × (Mean − Mode) = \(\frac{1}{3}\) × 12 = 4.
Median = Mean − 4 = 72 − 4 = 68.
Check with the empirical relation Mode = 3 Median − 2 Mean: 3 × 68 − 2 × 72 = 204 − 144 = 60, which matches.
Hence, the answer is 68.
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Important Questions from Measures of Central Tendency
A random sample of 20 people is classified in the following table according to their ages:
Age
Frequency
15 – 25
2
25 – 35
4
35 – 45
6
45 – 55
5
55 - 65
3
What is the mean age of this group of people?
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If the mode of the scores 10, 12, 13, 15, 15, 13, 12, 10, x is 15, then what is the value of x?
