find the variance of these data values: 212, 170, 199, 213, 173, 172, 184, 184, 214, 186, 180, 209, 199, 184, 170, 195, 193, 204

To calculate the variance of the given data values, we follow these steps:

### 1. **Find the mean (average)** of the dataTo calculate the variance of the given data values, we follow these steps:

### 1. **Find the mean (average)** of the 
\[
\text{Mean} = \frac{\text{Sum of all data values}}{\text{Number of data values}}
\]

The data values are:  
212, 170, 199, 213, 173, 172, 184, 184, 214, 186, 180, 209, 199, 184, 170, 195, 193, 204

Let's compute the mean:

\[
\text{Mean} = \frac{212 + 170 + 199 + 213 + 173 + 172 + 184 + 184 + 214 + 186 + 180 + 209 + 199 + 184 + 170 + 195 + 193 + 204}{18}
\]

### 2. **Compute each data point's deviation from the mean**, and square it to remove negative values.

### 3. **Calculate the average of these squared deviations**. This is the variance.

I'll calculate this now.The variance of the given data values is approximately \( 219.69 \).

Would you like further details on any step or have any questions?

Here are 5 follow-up questions to expand your understanding:
1. How do you calculate standard deviation from variance?
2. What does a higher variance indicate in a data set?
3. How is variance different from mean absolute deviation?
4. Why do we square the deviations when calculating variance?
5. How would you interpret variance in real-world applications?

**Tip:** Variance gives you a sense of how spread out data points are from the mean; the higher the variance, the more spread out the data.

Find the variance of these data values: 212, 170, 199, 213, 173, 172, 184, 184, 214, 186, 180, 209, 199, 184, 170, 195, 193, 204

Learn how to calculate the variance of the data set: 212, 170, 199, 213, 173, 172, 184, 184, 214, 186, 180, 209, 199, 184, 170, 195, 193, 204. This solution walks through finding the mean, calculating squared deviations, and finding the variance, suitable for students in Grades 9-12.

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