if there is 15 value equal to 15 then what is the standard deviation of this val

1. ### Break Down the Problem

To find the standard deviation of a set of values, we first identify the characteristics of the data:

• We have 15 values, and all of them are equal to 15.

2. ### Relevant Concepts

Standard deviation measures the dispersion or variability of a set of values from their mean. The formula for standard deviation $\sigma$ for a population is given by: $\sigma = \sqrt{\frac{\sum (x_i - \mu)^2}{N}}$ where:

• $x_i$ are the data points,
• $\mu$ is the mean of the data points,
• $N$ is the number of data points.

3. ### Analysis and Detail

1. Determine the Mean ($\mu$): Since all values are equal to 15, the mean $\mu$ is: $\mu = 15$

2. Calculate each deviation from the mean: $x_i - \mu = 15 - 15 = 0 \quad \text{for all } i$

3. Compute the variance $\sigma^2$: $\sigma^2 = \frac{\sum (x_i - \mu)^2}{N} = \frac{0^2 + 0^2 + \ldots + 0^2}{15} = \frac{0}{15} = 0$

4. Standard Deviation $\sigma$: $\sigma = \sqrt{0} = 0$

4. ### Verify and Summarize

Since all values are identical, the variability is 0, and thus the standard deviation is also 0.

Final Answer

The standard deviation of the 15 values, all equal to 15, is $0$.