CLASS INTERVAL $0-7$ $7-14$ $14-21$ $21-28$ $28-35$ $35-42$ $42-49$ FREQUENCY $19$ $25$ $36$ $72$ $51$ $43$ $28$ The arithmetic mean for the following frequency distribution is

Using the assumed mean method, let the assumed mean A be 21 (the midpoint of the third class). The class midpoints are 3.5, 10.5, 17.5, 24.5, 31.5, 38.5, and 45.5, yielding deviations of -17.5, -10.5, -3.5, 3.5, 10.5, 17.5, and 24.5. Multiplying these deviations by their frequencies gives -332.5, -262.5, -126, 252, 535.5, 752.5, and 686, which sum to 1505. Dividing this by the total frequency of 274 gives a mean deviation of approximately 5.49, and adding this to the assumed mean of 21 results in 26.5.

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