Question

The mean and S.D. of the scores of 100 candidates were found to be 80 and 15 respectively. Later, it was discovered that a score of 50 was wrongly read as 40. The correct mean and S.D. respectively are ______ 

Options

• 14.76, 80.1

• 80.1, 14.76

• 80.1, 217.99

• 217.99, 80.1

Answer 1

The mean and S.D. of the scores of 100 candidates were found to be 80 and 15 respectively. Later, it was discovered that a score of 50 was wrongly read as 40. The correct mean and S.D. respectively are 80.1, 14.76.

Explanation:

Corrected ∑x = 80 × 100 - 40 + 50 = 8010

∴ Corrected = `overlinex = 8010/100 = 80.1`

Incorrect ∑x² 

= `n[sigma^2 + overlinex^2] = 100[15^2 + 80^2] = 662500`

Corrected ∑x²

= 662500 - 1600 + 2500

= 663400

∴ Corrected `sigma = sqrt(663400/100 - (80.10)^2) = 14.76`