https://file.aiquickdraw.com/mathbot/file/17262161240412ew64166.jpg

To solve this problem, we need to determine two things:

1. Which cricketer has a better average?
2. Which cricketer is more consistent?

### Step 1: Calculate the average for each cricketer
The average score is calculated by summing all the scores and dividing by the total number of innings (which is 10 in this case).

For Cricketer A:
\[
\text{Average of A} = \frac{5 + 20 + 90 + 76 + 102 + 90 + 6 + 108 + 20 + 16}{10}
\]

For Cricketer B:
\[
\text{Average of B} = \frac{40 + 35 + 60 + 62 + 58 + 76 + 42 + 30 + 30 + 20}{10}
\]

### Step 2: Measure consistency
Consistency can be measured by calculating the **standard deviation** of the scores. A lower standard deviation means the scores are closer to the mean, indicating more consistency.

The formula for standard deviation is:
\[
\sigma = \sqrt{\frac{1}{n} \sum_{i=1}^{n} (x_i - \mu)^2}
\]
Where:
- \( x_i \) are the scores,
- \( \mu \) is the average,
- \( n \) is the number of innings (which is 10 here).

Let's calculate both the averages and the standard deviations for Cricketers A and B. I will compute this now.Here are the results:

1. **Average scores**:
   - Cricketer A: \(53.3\)
   - Cricketer B: \(45.3\)

   Cricketer A has a higher average score, so Cricketer A is better in terms of average.

2. **Standard deviations** (measuring consistency):
   - Cricketer A: \(40.93\)
   - Cricketer B: \(16.89\)

   Cricketer B has a lower standard deviation, indicating that Cricketer B is more consistent.

### Conclusion:
- **Better in average**: Cricketer A
- **More consistent**: Cricketer B

Would you like more details or have any questions?

Here are 5 related questions you might explore:
1. How does median compare to average in this data set for each cricketer?
2. What happens to the consistency if we remove the highest and lowest scores for each cricketer?
3. How would these statistics change if we add another inning with a new score?
4. How does variance differ from standard deviation, and how could we use it here?
5. Can we make any assumptions about their performance trends over time?

**Tip**: Standard deviation gives a good sense of how scores vary around the average, but sometimes looking at outliers can provide more context!

The number of runs scored by two cricketers A and B in 10 innings of 5 test matches are shown. Find which cricketer is (i) better in average, (ii) more consistent.

This problem involves determining the average and consistency of runs scored by two cricketers over 10 innings. By calculating both the average and the standard deviation, the problem shows which cricketer performs better and which one is more consistent.

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