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.