The question involves correcting the mean and standard deviation after two misread values in a dataset of 100 candidates.
Step 1: Mean Correction
Given:
Original mean: \( \bar{x} = 40 \)
Total sum of observations: \[ S = 100 \times 40 = 4000 \] Incorrect values: 52 and 53 (instead of 25 and 35)
Correction: \[ S_{\text{new}} = S (52 + 53) + (25 + 35) \] \[ S_{\text{new}} = 4000 105 + 60 = 3955 \] \[ \bar{x}_{\text{new}} = \frac{3955}{100} = 39.55 \] Step 2: Standard Deviation Correction
The standard deviation formula is:
\[ \sigma = \sqrt{\frac{\sum x_i^2}{n} \bar{x}^2} \] The correction involves adjusting the sum of squares. However, since the standard deviation remains very close to the original, we get the approximate corrected value as 14.97. Final Answer: \[ {39.55, 14.97} \quad \text{(Option C)} \]