Calculate the standard deviation of these numbers 21,18,21,25,27,23

To calculate the standard deviation, follow these steps:

### Step 1: Find the mean (average)
\[
\text{Mean} = \frac{\text{Sum of all numbers}}{\text{Total count of numbers}} = \frac{21 + 18 + 21 + 25 + 27 + 23}{6} = \frac{135}{6} = 22.5
\]

### Step 2: Find the squared differences from the mean
For each number, subtract the mean and square the result:

\[
(21 - 22.5)^2 = (-1.5)^2 = 2.25
\]
\[
(18 - 22.5)^2 = (-4.5)^2 = 20.25
\]
\[
(21 - 22.5)^2 = (-1.5)^2 = 2.25
\]
\[
(25 - 22.5)^2 = (2.5)^2 = 6.25
\]
\[
(27 - 22.5)^2 = (4.5)^2 = 20.25
\]
\[
(23 - 22.5)^2 = (0.5)^2 = 0.25
\]

### Step 3: Find the average of these squared differences (variance)
\[
\text{Variance} = \frac{2.25 + 20.25 + 2.25 + 6.25 + 20.25 + 0.25}{6} = \frac{51.5}{6} \approx 8.58
\]

### Step 4: Take the square root of the variance (standard deviation)
\[
\text{Standard deviation} = \sqrt{8.58} \approx 2.93
\]

So, the standard deviation of the numbers is approximately **2.93**.

Would you like more details or have any questions?

Here are 5 related questions:
1. How does the standard deviation differ from variance?
2. What is the significance of a high or low standard deviation?
3. How does standard deviation relate to data dispersion?
4. What are some applications of standard deviation in real-world scenarios?
5. How would the result change if an outlier was added to the dataset?

**Tip:** The standard deviation is sensitive to outliers, so large deviations from the mean can significantly affect its value.

Calculate the standard deviation of these numbers 21, 18, 21, 25, 27, 23

Learn how to calculate the standard deviation for the dataset 21, 18, 21, 25, 27, 23. This problem covers key statistical concepts like mean, variance, and standard deviation, suitable for students in Grades 9-12.

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