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To solve this problem, we need to follow these steps:

1. **Calculate the Mean** of the given data.
2. **Calculate the Standard Deviation** of the data.
3. **Identify the Scores** that are more than one standard deviation away from the mean.

Let's go through the calculations.

### Step 1: Calculate the Mean

The data set provided is:
\[ 52, 13, 108, 72, 19, 11, 21, 13, 28, 0, 10 \]

To find the mean (\(\mu\)):
\[
\mu = \frac{\sum \text{scores}}{\text{number of scores}} = \frac{52 + 13 + 108 + 72 + 19 + 11 + 21 + 13 + 28 + 0 + 10}{11}
\]

### Step 2: Calculate the Standard Deviation

1. Find the difference between each score and the mean.
2. Square these differences.
3. Find the average of these squared differences.
4. Take the square root of this average.

### Step 3: Identify Scores more than One Standard Deviation from the Mean

We'll determine which scores are greater than \(\mu + \sigma\) or less than \(\mu - \sigma\).

Let's calculate this.### Results

1. **Mean** of the scores: \( \mu \approx 31.55 \)
2. **Standard Deviation**: \( \sigma \approx 31.26 \)
3. **Scores more than one standard deviation away from the mean**: 
   - 108 (greater than \( \mu + \sigma \))
   - 72 (greater than \( \mu + \sigma \))
   - 0 (less than \( \mu - \sigma \))

**Total number of scores more than one standard deviation away from the mean:** 3.

Would you like further details or have any questions?

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Here are 5 related questions:

1. How do you interpret the standard deviation in a data set?
2. What would happen to the standard deviation if all the scores were increased by a constant value?
3. Can you determine how many scores are within one standard deviation of the mean?
4. How would the result change if one of the outlier scores was removed?
5. What does it mean for a score to be "more than one standard deviation away from the mean"?

**Tip:** Knowing how to calculate and interpret standard deviation is crucial in statistics, as it provides insight into the spread or dispersion of data points in a data set.

The number of runs scored by each batter in a cricket team are shown: 52, 13, 108, 72, 19, 11, 21, 13, 28, 0, 10. How many scores were more than one standard deviation away from the mean?

Determine the number of cricket scores that are more than one standard deviation away from the mean using standard statistical calculations. This problem involves finding the mean and standard deviation of a data set and identifying the scores that deviate significantly.

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