Multiple choice

Find the mean of the following data, by using the assumed mean method. Class Interval $0-10$ $10-20$ $20-30$ $30-40$ $40-50$ Frequency $7$ $8$ $12$ $13$ $10$

  1. $10$
  2. $30$
  3. $27.2$

  4. None of these
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C Correct answer
Explanation

Midpoints (x) are 5, 15, 25, 35, 45. Frequencies (f) are 7, 8, 12, 13, 10. Sum of f = 50. Sum of fx = 35 + 120 + 300 + 455 + 450 = 1360. Mean = 1360 / 50 = 27.2.

AI explanation

Using the assumed mean method, let the assumed mean A be 25 for the class marks 5, 15, 25, 35 and 45. The deviations (di) are -20, -10, 0, 10 and 20, yielding a sum of f_i_d_i equal to (7*-20) + (8*-10) + (12*0) + (13*10) + (10*20) = 110. The total frequency is 7 + 8 + 12 + 13 + 10 = 50. The mean is A + (sum of f_i_d_i divided by N), which calculates to 25 + (110 divided by 50), equaling 27.2.

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