2022 · Q49
Consider the following frequency distribution for the next three (03) items that follow: The values of x are 0, 1, 2, 3, 4, 5 with corresponding frequencies 46, p, q, 25, 10, 5. The total frequency is 200 and the mean of the distribution is 1.46. What is the value of q?
Elementary MathematicsStatistics
- A32
- B34
- C36
- D38
Explanation
The frequencies must sum to 200: 46 + p + q + 25 + 10 + 5 = 200, so p + q = 114. The mean equation gives (0×46 + 1×p + 2×q + 3×25 + 4×10 + 5×5)/200 = 1.46, i.e. p + 2q + 140 = 292, so p + 2q = 152. Subtracting the first equation from the second eliminates p: q = 152 − 114 = 38. Then p = 76, which is consistent with both equations. Hence option (D) 38.