Consider the following grouped frequency distribution: | x (Observation) | f (Frequency) | | --- | --- | | 0 - 10 | 8 | | 10 - 20 | 12 | | 20 - 30 | 10 | | 30 - 40 | P | | 40 - 50 | 9 | If the mean of the above data is 25.2, then what is the value of P?

Using the assumed mean method or direct formula, the sum of the frequencies is 39 plus P. The midpoints are 5, 15, 25, 35, and 45, so the sum of the products of frequency and midpoint is (8 times 5) plus (12 times 15) plus (10 times 25) plus (P times 35) plus (9 times 45), which totals 705 plus 35P. Setting the mean equation (705 plus 35P) divided by (39 plus P) equal to 25.2 gives 705 plus 35P equals 982.8 plus 25.2P. Solving this linear equation, 9.8P equals 107.8, so P is 11.

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