The problem asks us to calculate the standard deviation of the numbers 15, 21, 17, 26, 18, and 29, given that their mean is 21.

1. Problem Description

The problem asks us to calculate the standard deviation of the numbers 15, 21, 17, 26, 18, and 29, given that their mean is

2

1.

2. Solution Steps

First, let's write down the formula for the standard deviation.

$SD = \sqrt{\frac{\sum_{i=1}^{n}(x_i - \mu)^2}{n}}$, where $x_i$ are the individual data points, $\mu$ is the mean, and $n$ is the number of data points.

In our case, $n = 6$, $\mu = 21$, and $x_i$ are 15, 21, 17, 26, 18, and

2

9.

Now, we calculate the squared differences from the mean:

$(15 - 21)^2 = (-6)^2 = 36$

$(21 - 21)^2 = (0)^2 = 0$

$(17 - 21)^2 = (-4)^2 = 16$

$(26 - 21)^2 = (5)^2 = 25$

$(18 - 21)^2 = (-3)^2 = 9$

$(29 - 21)^2 = (8)^2 = 64$

Next, we sum these squared differences:

$\sum_{i=1}^{6}(x_i - \mu)^2 = 36 + 0 + 16 + 25 + 9 + 64 = 150$

Now, we divide by $n = 6$:

$\frac{\sum_{i=1}^{6}(x_i - \mu)^2}{n} = \frac{150}{6} = 25$

Finally, we take the square root:

$SD = \sqrt{25} = 5$

3. Final Answer

The standard deviation is

5. So the answer is C.