Mean of N numbers is X̅, the new mean when each number is multiplied by k is

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Bihar STET TGT (Maths) Official Paper-I (Held On: 04 Sept, 2023 Shift 1)
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  1. k X̅
  2. \(\rm \frac{\bar X}{k}\)
  3. X̅ + k
  4. X̅ - k

Answer (Detailed Solution Below)

Option 1 : k X̅
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Bihar STET Paper 1 Mathematics Full Test 1
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Detailed Solution

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Concept use:

Mean of Numbers = sum of observation/Total no of observation.

Calculations:

Mean of N numbers is X̅ 

Let the numbers are x1, x2, ........, xn 

Mean = xx ........ + xn / n = X̅      ------(1)

If each number is multiplied by k then the numbers are kx1, kx2, ........, kxn 

new Mean = kx1  kx2 + ........+ kxn / n = k(xx ........ + xn / n) = kX̅     from (1)

Hence, The Correct Answer is kX̅.

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