18 – 34		35 – 44		45 and Older
1,355			969			1,135	
115			434			956	
1,456			1,792			400	
2,045			1,500			1,374	
1,621			1,277			1,244	
994			1,056			825	
1,937			1,922			763	
1,200			1,350			1,192	
1,567			1,586			1,305	
1,390			1,415			1,510	
a. Compute the mean, variance, and standard deviation for each of these three samples. Round your answers to one decimal place.

To compute the mean, variance, and standard deviation for each of the three age groups (18-34, 35-44, and 45 and older), we will:

1. **Mean (average)**: Sum all the values and divide by the number of values.
   
   \[
   \text{Mean} = \frac{\sum{x_i}}{n}
   \]

2. **Variance**: The average of the squared differences from the mean. The formula is:
   
   \[
   \text{Variance} = \frac{\sum{(x_i - \mu)^2}}{n}
   \]
   
3. **Standard Deviation**: The square root of the variance.
   
   \[
   \text{Standard Deviation} = \sqrt{\text{Variance}}
   \]

Where \(x_i\) are the data points, \(\mu\) is the mean, and \(n\) is the number of data points.

Let's calculate for each age group. The data points for each group are:

- **18-34**: 1,355, 115, 1,456, 2,045, 1,621, 994, 1,937, 1,200, 1,567, 1,390
- **35-44**: 969, 434, 1,792, 1,500, 1,277, 1,056, 1,922, 1,350, 1,586, 1,415
- **45 and Older**: 1,135, 956, 400, 1,374, 1,244, 825, 763, 1,192, 1,305, 1,510

I'll calculate these now.Here are the computed mean, variance, and standard deviation for each age group:

### 18–34:
- **Mean**: 1368.0
- **Variance**: 263,220.6
- **Standard Deviation**: 513.1

### 35–44:
- **Mean**: 1330.1
- **Variance**: 167,699.1
- **Standard Deviation**: 409.5

### 45 and Older:
- **Mean**: 1070.4
- **Variance**: 100,679.4
- **Standard Deviation**: 317.3

Would you like further details or have any questions?

Here are five related questions to expand your understanding:
1. How does the range of data affect the standard deviation?
2. What is the difference between population variance and sample variance?
3. How does variance change when the mean increases?
4. How can we use these statistics in making decisions?
5. Why is the standard deviation a more intuitive measure than variance?

**Tip**: Standard deviation is often more meaningful than variance because it is in the same units as the data.

Compute the mean, variance, and standard deviation for each of these three samples: 18–34, 35–44, and 45 and Older age groups.

This page provides step-by-step calculations for the mean, variance, and standard deviation of three age groups: 18–34, 35–44, and 45 and Older. It includes formulas and explanations to help understand key statistical concepts, suitable for students in Grades 9-12.

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