The data to the right contain the state cigarette tax​ (in $) for all 20 regions of a country. 1.36
1.75
2.52
0.44
1.03
0.62
3.00
0.57
2.00
0.84
1.56
0.98
0.36
2.00
4.35
0.60
2.70
1.70
1.41
0.87    Compute the population mean and population standard deviation for the state cigarette tax.

To compute the population mean and the population standard deviation, we follow these steps:

### Step 1: Compute the Population Mean
The population mean $\mu$ is given by the formula:

\[
\mu = \frac{\sum_{i=1}^{N} x_i}{N}
\]

Where:
- $x_i$ represents each value of the dataset.
- $N$ is the total number of data points.

### Step 2: Compute the Population Standard Deviation
The population standard deviation $\sigma$ is calculated using the formula:

\[
\sigma = \sqrt{\frac{\sum_{i=1}^{N} (x_i - \mu)^2}{N}}
\]

Let's compute these values based on the provided dataTo compute the population mean and the population standard deviation, we follow these steps:

### Step 1: Compute the Population Mean
The population mean $\mu$ is given by the formula:

\[
\mu = \frac{\sum_{i=1}^{N} x_i}{N}
\]

Where:
- $x_i$ represents each value of the dataset.
- $N$ is the total number of data points.

### Step 2: Compute the Population Standard Deviation
The population standard deviation $\sigma$ is calculated using the formula:

\[
\sigma = \sqrt{\frac{\sum_{i=1}^{N} (x_i - \mu)^2}{N}}
\]

Let's compute these values based on the provided 

**Data Set:**  
1.36, 1.75, 2.52, 0.44, 1.03, 0.62, 3.00, 0.57, 2.00, 0.84,  
1.56, 0.98, 0.36, 2.00, 4.35, 0.60, 2.70, 1.70, 1.41, 0.87

Now, I'll calculate both the mean and standard deviation.The population mean of the state cigarette tax is approximately **$1.533**.  
The population standard deviation is approximately **$0.991**.

Would you like more details or have any questions about these calculations?

Here are some related questions you might explore:
1. What is the variance of the data?
2. How does the sample standard deviation differ from the population standard deviation?
3. How would outliers affect the mean and standard deviation in this data set?
4. Can you compute the median cigarette tax for this data?
5. How can we visualize this data (e.g., histogram, box plot)?

**Tip:** When analyzing data, the mean gives a central value, but the standard deviation tells you how spread out the values are. Both are important for understanding the distribution.

The data to the right contain the state cigarette tax​ (in $) for all 20 regions of a country. 1.36, 1.75, 2.52, 0.44, 1.03, 0.62, 3.00, 0.57, 2.00, 0.84, 1.56, 0.98, 0.36, 2.00, 4.35, 0.60, 2.70, 1.70, 1.41, 0.87. Compute the population mean and population standard deviation for the state cigarette tax.

Learn how to compute the population mean and standard deviation for state cigarette taxes using a data set of 20 values. This example explains key statistical concepts like central tendency and data dispersion, suitable for students in Grades 9-12.

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