Discussion

Find the mean of the distribution given below.

Value (x)	4	6	9	10	15
Frequency (f)	5	10	10	7	8

Answer: A

Correct answer: 9.000

For a frequency distribution the mean is the total of \(f_i x_i\) divided by the total frequency.

\[\sum f_i x_i = (4\times 5) + (6\times 10) + (9\times 10) + (10\times 7) + (15\times 8)\]

\[= 20 + 60 + 90 + 70 + 120 = 360\]

\[\sum f_i = 5 + 10 + 10 + 7 + 8 = 40\]

\[\text{Mean} = \frac{360}{40} = 9\]

Averaging the values alone, ignoring their frequencies, would give \(\tfrac{44}{5} = 8.8\) - the usual error here.

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