For the grouped data 100–120: 12, 120–140: 14, 140–160: 8, 160–180: 6, 180–200: 10 (class interval: frequency), find the mean by the step-deviation method with assumed mean A = 150 and h = 20.

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145.2. The class marks are 110, 130, 150, 170, 190, so u = (x − 150)/20 takes the values −2, −1, 0, 1, 2. Then Σfu = 12(−2) + 14(−1) + 8(0) + 6(1) + 10(2) = −12 with Σf = 50. Mean = A + h × (Σfu/Σf) = 150 + 20 × (−12/50) = 150 − 4.8 = 145.2. Forgetting to multiply by h gives 149.76; using the wrong sign gives 154.8.

For the grouped data 100–120: 12, 120–140: 14, 140–160: 8, 160–180: 6, 180–200: 10 (class interval: frequency), find the mean by the step-deviation method with assumed mean A = 150 and h = 20.

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