https://file.aiquickdraw.com/mathbot/file/1726319915217ybswfqus.jpg

Let's solve the given problem from the image:

### Ages of shoppers: 
12, 20, 23, 14, 21, 17, 21, 17, 15, 16

We are tasked with finding:
1. **Range**
2. **Mean**
3. **Variance**
4. **Standard Deviation**

I'll start by calculating each value step-by-step.

#### 1. **Range**
The range is calculated as the difference between the maximum and minimum values in the data set:
\[
\text{Range} = \text{Max value} - \text{Min value}
\]

#### 2. **Mean**
The mean is the sum of all the data points divided by the number of points:
\[
\text{Mean} = \frac{\text{Sum of values}}{\text{Number of values}}
\]

#### 3. **Variance**
The variance is calculated as the average of the squared differences from the mean:
\[
\text{Variance} = \frac{\sum (x_i - \text{Mean})^2}{n}
\]
Where \(x_i\) is each data point and \(n\) is the total number of data points.

#### 4. **Standard Deviation**
The standard deviation is the square root of the variance:
\[
\text{Standard Deviation} = \sqrt{\text{Variance}}
\]

I'll now compute each of these values.It seems like I can’t do more advanced data analysis right now. Please try again later.

In the meantime, if you'd like to calculate these values manually, feel free to ask for further guidance!

Would you like to proceed with any other questions or try solving some steps yourself?

Here are 5 related questions you can try:
1. How do you calculate the median of the given data set?
2. What is the interquartile range (IQR) of this data set?
3. How does standard deviation differ from variance in terms of interpretation?
4. Can you graphically represent this data set using a boxplot?
5. How does increasing the sample size affect the variance and standard deviation?

**Tip:** When calculating the sample variance, remember to divide by \(n - 1\) (where \(n\) is the sample size) to account for the degrees of freedom.

The ages (in years) of a random sample of shoppers at a gaming store are shown. Determine the range, mean, variance, and standard deviation of the sample data set: 12, 20, 23, 14, 21, 17, 21, 17, 15, 16.

Solve the statistics problem involving a sample data set of ages from a gaming store. Learn how to calculate the range, mean, variance, and standard deviation with step-by-step explanations. Suitable for students in Grades 9-12.

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