calculate the standard deviation of the following numbers if their mean is 1.22:  1, 1.2, 1 , 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1.5, 1, 1, 1, 1.1, 1.2, 1, 2, 1, 1, 1, 1.3 , 1, 1.4, 1, 1.3, 1, 1.2, 1.5, 1.1, 1, 1, 1, 1.1, 2, 1.2, 1.3, 1.3, 1.2, 1, 1, 1, 1, 1, 1, 1.2, 1, 1, 1.5, 1.2, 1, 1, 1, 1.3, 1.1, 1.1, 2, 1, 1.8, 1, 1.2, 1.1, 1, 1, 1, 1.2, 1, 1.3, 1.4, 1.8, 1.9, 1.1, 1.1, 1.1, 1, 2, 1, 1.2, 1.3, 1.1, 1.3, 1.1, 1.1, 1, 1.2, 1, 1.2, 1.2, 2.1, 1.3, 1.1, 1, 1, 1.1, 1.2, 2.2, 2.1.

To calculate the standard deviation of a set of numbers, given their mean, follow these steps:

1. **Find the squared deviations**: Subtract the mean from each number and square the result.
2. **Average the squared deviations**: This gives the variance.
3. **Take the square root of the variance**: This gives the standard deviation.

Let's calculate the standard deviation for the given numbers, where the mean is \( \mu = 1.22 \):

The formula for the standard deviation \( \sigma \) is:

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

Where:
- \( N \) is the total number of data points.
- \( x_i \) is each individual data point.
- \( \mu \) is the mean.

Let me calculate that for you.The standard deviation of the given numbers is approximately \( 0.318 \).

Would you like further details on how this was calculated or have any other questions?

Here are some related questions to explore:
1. How does the standard deviation change if the dataset becomes more spread out?
2. What is the difference between standard deviation and variance?
3. How can you use standard deviation to determine the spread of a dataset?
4. How does standard deviation differ in populations vs. samples?
5. Why is standard deviation important in fields like finance or science?

**Tip**: A smaller standard deviation means the data points are closer to the mean, indicating less variability in the dataset.

calculate the standard deviation of the following numbers if their mean is 1.22: 1, 1.2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1.5, 1, 1, 1, 1.1, 1.2, 1, 2, 1, 1, 1, 1.3 , 1, 1.4, 1, 1.3, 1, 1.2, 1.5, 1.1, 1, 1, 1, 1.1, 2, 1.2, 1.3, 1.3, 1.2, 1, 1, 1, 1, 1, 1, 1.2, 1, 1, 1.5, 1.2, 1, 1, 1, 1.3, 1.1, 1.1, 2, 1, 1.8, 1, 1.2, 1.1, 1, 1, 1, 1.2, 1, 1.3, 1.4, 1.8, 1.9, 1.1, 1.1, 1.1, 1, 2, 1, 1.2, 1.3, 1.1, 1.3, 1.1, 1.1, 1, 1.2, 1, 1.2, 1.2, 2.1, 1.3, 1.1, 1, 1, 1.1, 1.2, 2.2, 2.1.

Learn how to calculate the standard deviation for a data set with a mean of 1.22. This step-by-step guide covers the standard deviation formula, variance, and statistical concepts involved. Suitable for students in Grades 10-12.

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