JEE Main · 2025 · 07 Apr 2025 · Shift 1 · Statistics

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The mean and standard deviation of 100 observations are 40 and 5.1, respectively. By mistake one observation is taken as 50 instead of 40. If the correct mean and the correct standard deviation are

μ

and

σ

respectively, then

10 (μ + σ)

is equal to

(A)445
(B)451
(C)447
(D)449✓ Correct

Answer: (D)

Solution

The faulty total is

100 \times 40 = 4000

; replacing the wrong entry

50

by the true

40

gives the correct total

3990

, so

μ = 39.9

. From the faulty data

\sum x_{i}^{2} = 100 (5. 1^{2} + 4 0^{2}) = 162601

, and correcting the one entry gives

\sum x_{i}^{2} = 162601 - 5 0^{2} + 4 0^{2} = 161701

. The correct variance is

\frac{161701}{100} - 39. 9^{2} = 1617.01 - 1592.01 = 25

, so

σ = 5

. Therefore

10 (μ + σ) = 10 (39.9 + 5) = 449

JEE Main · 2025 · 07 Apr 2025 · Shift 1 · Single correct option

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