The data to the right contain the state cigarette tax​ (in $) for all 20 regions of a country.
1.36
1.75
2.51
0.45
1.18
0.64
3.00
0.55
2.00
0.79
1.60
0.98
0.37
2.24
4.35
0.62
2.70
1.78
1.53
0.84  Compute the population mean and population standard deviation for the regional cigarette taxes.

To calculate the **population mean** and the **population standard deviation** for the given regional cigarette taxes, follow these steps:

### 1. Population Mean ( $\mu$ )
The population mean is the sum of all data values divided by the number of values.

\[
\mu = \frac{\sum{x_i}}{N}
\]
Where:
- $x_i$ are the individual data points.
- $N$ is the total number of data points (20 in this case).

### 2. Population Standard Deviation ( $\sigma$ )
The population standard deviation is calculated using the following formula:

\[
\sigma = \sqrt{\frac{\sum{(x_i - \mu)^2}}{N}}
\]
Where:
- $x_i$ are the individual data points.
- $\mu$ is the population mean.
- $N$ is the total number of data points.

Let me calculate these for you.The **population mean** of the regional cigarette taxes is approximately **1.562** dollars, and the **population standard deviation** is approximately **0.996** dollars.

Would you like a more detailed explanation of the calculations? Here are 5 related questions that expand on this topic:

1. How is the population standard deviation different from the sample standard deviation?
2. How would the calculations change if this were a sample rather than the entire population?
3. What does the standard deviation tell us about the distribution of cigarette taxes?
4. Can we use this data to infer anything about regional economic differences?
5. How do outliers affect the mean and standard deviation?

**Tip:** The standard deviation helps measure the spread of the data around the mean. A larger value indicates greater variability.

The data to the right contain the state cigarette tax​ (in $) for all 20 regions of a country. 1.36, 1.75, 2.51, 0.45, 1.18, 0.64, 3.00, 0.55, 2.00, 0.79, 1.60, 0.98, 0.37, 2.24, 4.35, 0.62, 2.70, 1.78, 1.53, 0.84. Compute the population mean and population standard deviation for the regional cigarette taxes.

Learn how to compute the population mean and standard deviation for regional cigarette taxes in a country. Data includes values like 1.36, 1.75, 2.51, and more. This problem demonstrates key statistical concepts and is suitable for high school students (Grades 9-12).

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