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In a frequency table the value k occurs exactly k times, for k = 1, 2, 3, …, 20. What is the mean of the distribution?

Competition practiceStatistics

A14
B $13 \frac{1}{3}$
C $13 \frac{2}{3}$
D10.5

Step-by-Step Solution

Σ f x = Σ k^{2} = \frac{20 \cdot 21 \cdot 41}{6} = 2870

and

Σ f = Σ k = 210

. Mean

= \frac{2870}{210} = \frac{41}{3} = 13 \frac{2}{3}

. (10.5 ignores the frequencies.)

Answer: C)

13 \frac{2}{3}

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