The mean of 40 observations grouped in a frequency table is 30. One more class 80-100 is now appended with frequency k, and the mean of all the observations becomes 40. Find k.

Question

Accepted Answer

8. The old total is f_i x_i = 30 × 40 = 1200 ; the new class adds 90k (90 is its class mark). So 1200 + 90k/40 + k = 40 , i.e. 1200 + 90k = 1600 + 40k, giving 50k = 400 and k = 8. "10" uses the lower limit 80 as the class mark; "6.67" uses the upper limit 100; "400" stops at 50k = 400 without dividing.

The mean of 40 observations grouped in a frequency table is 30. One more class 80-100 is now appended with frequency k, and the mean of all the observations becomes 40. Find k.

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