The standard deviation of the numbers​ 2, 3,​ 4, 4, and 6 is approximately

To calculate the standard deviation of the numbers \(2, 3, 4, 4, 6\), we will follow these steps:

1. **Find the mean (average)**:
   \[
   \text{Mean} = \frac{2 + 3 + 4 + 4 + 6}{5} = \frac{19}{5} = 3.8
   \]

2. **Calculate the squared differences from the mean**:
   \[
   (2 - 3.8)^2 = (-1.8)^2 = 3.24
   \]
   \[
   (3 - 3.8)^2 = (-0.8)^2 = 0.64
   \]
   \[
   (4 - 3.8)^2 = (0.2)^2 = 0.04
   \]
   \[
   (4 - 3.8)^2 = (0.2)^2 = 0.04
   \]
   \[
   (6 - 3.8)^2 = (2.2)^2 = 4.84
   \]

3. **Find the average of these squared differences (the variance)**:
   \[
   \text{Variance} = \frac{3.24 + 0.64 + 0.04 + 0.04 + 4.84}{5} = \frac{8.8}{5} = 1.76
   \]

4. **Take the square root of the variance to get the standard deviation**:
   \[
   \text{Standard deviation} = \sqrt{1.76} \approx 1.33
   \]

The standard deviation of the numbers \(2, 3, 4, 4, 6\) is approximately \(1.33\).

Would you like more details or have any questions about this calculation?

Here are some related questions to deepen your understanding:
1. How is standard deviation different from variance?
2. What does a standard deviation of 1.33 imply about the spread of these numbers?
3. How would adding another number to this data set affect the standard deviation?
4. What are some real-life situations where standard deviation is used?
5. Can standard deviation ever be negative?

**Tip:** The standard deviation is a measure of how spread out the numbers in a data set are from the mean. A smaller standard deviation means the numbers are closer to the mean.

The standard deviation of the numbers 2, 3, 4, 4, and 6 is approximately

Learn how to calculate the standard deviation of the numbers 2, 3, 4, 4, and 6. This solution covers key statistical concepts, such as variance and standard deviation, with a detailed step-by-step guide. Suitable for students in Grades 8-10.

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