Question

Consider the runs scored by Virat Kohli in IPL 2025 as 90, 102, 115, 85, 90, 100, 110, 110 in the 9 matches. Find the standard deviation of the score.

• A. 10.2
• B. 104.22
• C. 101.33
• D. 102

Hint:

Notice the relationships in the options:
- Option C is the Mean (101.33).
- Option B is the Variance (104.22).
- Option A is the Standard Deviation (10.2), which is $\sqrt{\text{Variance}} \approx \sqrt{104.22}$.
Understanding these connections saves you calculation time!

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The question asks to find the standard deviation of the runs scored by a player. The question mentions 9 matches but lists only 8 scores explicitly: 90, 102, 115, 85, 90, 100, 110, 110. We must resolve this discrepancy to find the correct answer among the choices.

Step 2: Identifying the Missing Value and Computing Statistics:
Let us analyze the choices:
- Choice (C) is 101.33.
- Choice (B) is 104.22.
- Choice (A) is 10.2.
- If the mean score of the 9 matches is exactly 101.33 (which is $912 / 9$):
- The sum of all 9 scores must be: $9 \times 101.333 = 912$.
- Sum of the given 8 scores is: $90 + 102 + 115 + 85 + 90 + 100 + 110 + 110 = 802$.
- This indicates the missing 9th score is: $912 - 802 = 110$.
- Therefore, the complete dataset of 9 matches is: 90, 102, 115, 85, 90, 100, 110, 110, 110.

Step 3: Calculating Variance and Standard Deviation:
- Mean ($\mu$):
\[ \mu = \frac{912}{9} \approx 101.33 \]
- Deviations from the Mean ($x_i - \mu$):
- $90 - 101.33 = -11.33 \rightarrow (-11.33)^2 \approx 128.37$
- $102 - 101.33 = 0.67 \rightarrow (0.67)^2 \approx 0.45$
- $115 - 101.33 = 13.67 \rightarrow (13.67)^2 \approx 186.87$
- $85 - 101.33 = -16.33 \rightarrow (-16.33)^2 \approx 266.67$
- $90 - 101.33 = -11.33 \rightarrow (-11.33)^2 \approx 128.37$
- $100 - 101.33 = -1.33 \rightarrow (-1.33)^2 \approx 1.77$
- $110 - 101.33 = 8.67 \rightarrow (8.67)^2 \approx 75.17$
- $110 - 101.33 = 8.67 \rightarrow (8.67)^2 \approx 75.17$
- $110 - 101.33 = 8.67 \rightarrow (8.67)^2 \approx 75.17$
- Sum of Squared Deviations ($\sum (x_i - \mu)^2$):
\[ \sum (x_i - \mu)^2 = 128.37 + 0.45 + 186.87 + 266.67 + 128.37 + 1.77 + 75.17 + 75.17 + 75.17 = 938.01 \]
- Population Variance ($\sigma^2$):
\[ \sigma^2 = \frac{938.01}{9} = 104.22 \]
- Note that this matches Option (B) 104.22 exactly as the variance.
- Standard Deviation ($\sigma$):
\[ \sigma = \sqrt{104.22} \approx 10.21 \]
- This matches Option (A) 10.2 as the standard deviation.

Step 4: Final Answer:
The standard deviation of the player's runs is 10.2.
Hence, option (A) is the correct choice.