21.0	25.0	15.0	21.5	35.6	15.0
33.1	11.9	16.3	31.1	30.0   Find standard deviation

To find the standard deviation of the given dataset:

**Dataset:**
21.0, 25.0, 15.0, 21.5, 35.6, 15.0, 33.1, 11.9, 16.3, 31.1, 30.0

### Steps to calculate standard deviation:

1. **Find the mean (average):**
   \[
   \text{Mean} = \frac{\sum{x}}{n}
   \]
   where \( x \) are the data points, and \( n \) is the number of data points.

2. **Calculate the squared differences from the mean:**
   \[
   (x_i - \text{Mean})^2
   \]
   for each data point \( x_i \).

3. **Find the variance:**
   \[
   \text{Variance} = \frac{\sum{(x_i - \text{Mean})^2}}{n}
   \]
   (if this is a population standard deviation), or
   \[
   \text{Variance} = \frac{\sum{(x_i - \text{Mean})^2}}{n-1}
   \]
   (if this is a sample standard deviation).

4. **Find the standard deviation:**
   \[
   \text{Standard Deviation} = \sqrt{\text{Variance}}
   \]

Let's calculate this step by step.

### 1. Calculate the mean

\[
\text{Mean} = \frac{21.0 + 25.0 + 15.0 + 21.5 + 35.6 + 15.0 + 33.1 + 11.9 + 16.3 + 31.1 + 30.0}{11}
\]

Let me calculate the values.The mean (average) of the dataset is approximately \( 23.23 \).

### 2. Calculate the squared differences from the mean

Now, we will compute the squared differences for each data point from the mean and then find the variance. I'll calculate it next.The standard deviation of the dataset is approximately \( 8.25 \).

Would you like more details or have any questions about the process?

Here are some related questions:
1. How does standard deviation help in understanding data dispersion?
2. What is the difference between population and sample standard deviation?
3. How would the result change if this were a population instead of a sample?
4. Can you compute the variance from the standard deviation?
5. How does standard deviation relate to data spread and outliers?

**Tip:** A higher standard deviation means more variability in your data, while a lower standard deviation indicates the data points are closer to the mean.

21.0 25.0 15.0 21.5 35.6 15.0 33.1 11.9 16.3 31.1 30.0 Find standard deviation

Learn how to calculate the standard deviation of the dataset 21.0, 25.0, 15.0, 21.5, 35.6, 15.0, 33.1, 11.9, 16.3, 31.1, 30.0. This guide covers the steps to find the mean, variance, and standard deviation. Suitable for Grades 9-12 students.

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