451 412 419 412 375 397 429 454 407 375 393 357 456 467 426 355 345 439 364 432 381 414 392 451 413 425 422 421 329 413 L’écart type

To calculate the standard deviation (écart type) of the given data set, we follow these steps:

1. **Mean (average)**: First, find the mean of the numbers.
2. **Variance**: Then, calculate the squared differences from the mean.
3. **Standard Deviation**: Finally, take the square root of the variance.

Let’s calculate it step by step.

### Step 1: Find the mean
The given data set is:
\[ 451, 412, 419, 412, 375, 397, 429, 454, 407, 375, 393, 357, 456, 467, 426, 355, 345, 439, 364, 432, 381, 414, 392, 451, 413, 425, 422, 421, 329, 413 \]

The formula for the mean:
\[
\mu = \frac{\sum{x_i}}{n}
\]
Where:
- \(x_i\) are the individual data points.
- \(n\) is the number of data points.

Let me calculate this for you.The mean (average) of the data set is approximately \( 407.53 \).

### Step 2: Calculate the variance
Next, we calculate the squared differences from the mean, and then the variance.

The formula for variance is:
\[
\sigma^2 = \frac{\sum{(x_i - \mu)^2}}{n}
\]
Where:
- \(x_i\) are the data points.
- \(\mu\) is the mean.
- \(n\) is the number of data points.

Let me calculate the variance for you.It seems like I can’t do more advanced data analysis right now. Please try again later.

Would you like me to guide you through the steps of calculating the variance and standard deviation manually? Here are some relative questions you might want to explore

Learn how to calculate the standard deviation for the data set: 451, 412, 419, 412, 375, and more. This tutorial explains key concepts like mean, variance, and standard deviation, using step-by-step formulas. Perfect for students in Grades 9-12.

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