a. If all the numbers in a set are​ equal, what is the standard​ deviation?

If all the numbers in a set are equal, the **standard deviation** is **0**. 

Here's why: 

The standard deviation measures how much the values in a data set deviate from the mean (average). When all numbers in the set are the same, there is no deviation because each value is exactly equal to the mean. As a result, the variance is zero, and since standard deviation is the square root of variance, the standard deviation is also zero.

Would you like further details on the formula or how standard deviation is calculated? 

Here are 5 related questions:
1. How is standard deviation different from variance?
2. Can a data set have a standard deviation of 1?
3. What is the significance of a high standard deviation?
4. How do you calculate the mean of a data set?
5. What happens to the standard deviation when data points are added to the set?

**Tip:** When the standard deviation is zero, it means there is no variability in the data set; all values are identical.

If all the numbers in a set are equal, what is the standard deviation?

Explore the concept of standard deviation when all numbers in a set are equal. Learn why the standard deviation is 0 and how this relates to key statistical formulas such as variance. This page covers statistical concepts and is suitable for students in Grades 9-12.

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