We are given the jersey numbers of 11 players:
24, 40, 94, 21, 61, 83, 38, 88, 44, 27, 11

Part 1: Range

The range is the difference between the largest and smallest numbers in the data set.

• Largest number: 94
• Smallest number: 11

$\text{Range} = \text{Largest number} - \text{Smallest number} = 94 - 11 = 83$

The range is 83.

Part 2: Variance and Standard Deviation

We can calculate the variance $s^2$ and the standard deviation $s$ for the sample. The steps to calculate variance are:

1. Find the mean (average) of the sample.
2. Subtract the mean from each number, and square the result.
3. Sum all the squared results.
4. Divide the sum by $n - 1$ (degrees of freedom), where $n$ is the number of data points.

Let’s proceed with the calculations.### Results:

• Range: 83
• Variance: 840.4 (rounded to one decimal place)
• Standard Deviation: 29.0 (rounded to one decimal place)

Interpretation:

The range shows the difference between the largest and smallest jersey numbers is quite wide (83). The high variance and standard deviation indicate that the jersey numbers are spread out, with many numbers deviating significantly from the mean.

Would you like more details or have any questions?

Here are some related questions for further practice:

1. How do you calculate the median of this data set?
2. What is the interquartile range (IQR) of the jersey numbers?
3. How would the variance change if the highest number was much closer to the mean?
4. What effect does adding or subtracting a constant from each data point have on the standard deviation?
5. How does the variance differ from the standard deviation in terms of interpretation?

Tip: Standard deviation gives you a sense of how data is dispersed around the mean, and it is more useful than range for large datasets.