The mean of the following data is $18.75$ then the value of $p$ : Class mark $(x_i)$ $10$ $15$ $p$ $25$ $30$ Frequency $(f_i)$ $5$ $10$ $7$ $8$ $2$

Using the direct mean formula, the sum of the products of frequency and class mark divided by the total frequency equals the mean. The total frequency is 5 + 10 + 7 + 8 + 2 = 32. The equation is 18.75 = ((5*10) + (10*15) + (7*p) + (8*25) + (2*30)) divided by 32. Solving this gives 600 = 50 + 150 + 7p + 200 + 60, which simplifies to 7p = 140, so p = 20.

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