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Worked Examples · Example 5
Q.

Using the same wages data as Worked Example 4, find the mean wage using the step-deviation method, and verify it agrees with the assumed mean method's answer.

Wages (₹)100–120120–140140–160160–180180–200
Number of workers (ff)81215105
West Bengal WbchseTextbookSubjectiveImportance★★★★★est
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All five classes have the same width, h=20h = 20, so the step-deviation method applies: xˉ=A+h⋅∑fu∑f\bar{x} = A + h\cdot\dfrac{\sum fu}{\sum f}, where u=x−Ahu = \dfrac{x-A}{h}, using the same assumed mean A=150A = 150 as Worked Example 4.

Step 1 — Compute the step-deviations uu and fufu.

Classffxxd=x−150d=x-150u=d/20u=d/20fufu
100–1208110–40−2−16
120–14012130–20−1−12
140–16015150000
160–1801017020110
180–200519040210
Total50−8

∑fu=−16−12+0+10+10=−8\sum fu = -16-12+0+10+10 = -8.

Step 2 — Apply the formula. …

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