Central Tendency & DispersionPYQ Sep 24Question 2878 of 473
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The mean of group X is 70 and the mean of group Y is 85. If the number of observations in group Y is five times that of group X, then the combined mean of both the group is:

Options

A80
B75
C77.5
D82.5
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Correct Answer

✅ Option d — 82.5

All Options:

  • A80
  • B75
  • C77.5
  • D82.5

Detailed Solution & Explanation

**Step 1: Set up variables.** Let nX=n\displaystyle n_X = n (observations in group X). Then nY=5n\displaystyle n_Y = 5n (observations in group Y). **Step 2: Apply combined mean formula.** xˉcombined=nX⋅xˉX+nY⋅xˉYnX+nY\bar{x}_{combined} = \frac{n_X \cdot \bar{x}_X + n_Y \cdot \bar{x}_Y}{n_X + n_Y} =n×70+5n×85n+5n=70n+425n6n=495n6n=4956=82.5= \frac{n \times 70 + 5n \times 85}{n + 5n} = \frac{70n + 425n}{6n} = \frac{495n}{6n} = \frac{495}{6} = 82.5 Hence, **Option D** is the correct answer.

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