Step 1: Understanding the Concept:
Standard deviation is a measure of the amount of variation or dispersion of a set of values. It is calculated by taking the square root of the variance, where variance is the average of the squared differences from the Mean.
Step 2: Detailed Explanation:
The given scores are: 90, 102, 115, 85, 90, 100, 110, 110.
Sum of scores = \( 90 + 102 + 115 + 85 + 90 + 100 + 110 + 110 = 802 \).
Number of matches (n) = 8.
Mean (\( \mu \)) = \( 802 / 8 = 100.25 \).
Calculate variance \( \sigma^2 = \frac{\sum(x_i - \mu)^2}{n} \):
\( (90-100.25)^2 = 105.06 \)
\( (102-100.25)^2 = 3.06 \)
\( (115-100.25)^2 = 217.56 \)
\( (85-100.25)^2 = 232.56 \)
\( (90-100.25)^2 = 105.06 \)
\( (100-100.25)^2 = 0.06 \)
\( (110-100.25)^2 = 95.06 \)
\( (110-100.25)^2 = 95.06 \)
Sum of squares = \( 853.48 \).
Variance \( \sigma^2 = 853.48 / 8 = 106.685 \).
Standard Deviation \( \sigma = \sqrt{106.685} \approx 10.33 \).
(Note: Option (A) 10.2 is the closest approximation provided in the choices).
Step 3: Final Answer:
The closest value to the calculated standard deviation is 10.2.