Calculate the population standard deviation of the data 13, 17, 23, 26, 31, 28, 15, 34, 17, and 26.
(Round off your answer to two decimal places.)

The correct option is 6.81.

To find the population standard deviation of the given data set, we follow a step-by-step process:

Step 1: List the data points
The given data points are:
13, 17, 23, 26, 31, 28, 15, 34, 17, and 26.
The total number of data points (N) is 10.

Step 2: Calculate the population mean ($\mu$)
The mean is the sum of all data points divided by the total number of points:
$\mu =\frac{13+17+23+26+31+28+15+34+17+26}{10}$

$\mu =\frac{230}{10}=23$

Step 3: Calculate the squared deviation of each data point from the mean
For each data point $x_i$, we calculate ${(x_i-\mu )}^2$:
• For 13: ${(13-23)}^2={(-10)}^2=100$
• For 17: ${(17-23)}^2={(-6)}^2=36$
• For 23: ${(23-23)}^2={\left(0\right)}^2=0$
• For 26: ${(26-23)}^2={\left(3\right)}^2=9$
• For 31: ${(31-23)}^2={\left(8\right)}^2=64$
• For 28: ${(28-23)}^2={\left(5\right)}^2=25$
• For 15: ${(15-23)}^2={(-8)}^2=64$
• For 34: ${(34-23)}^2={\left(11\right)}^2=121$
• For 17: ${(17-23)}^2={(-6)}^2=36$
• For 26: ${(26-23)}^2={\left(3\right)}^2=9$

Step 4: Calculate the population variance (${\sigma }^2$)
The variance is the sum of these squared deviations divided by the population size (N = 10):
${\sigma }^2=\frac{100+36+0+9+64+25+64+121+36+9}{10}$

${\sigma }^2=\frac{464}{10}=46.4$

Step 5: Calculate the population standard deviation ($\sigma$)
The standard deviation is the square root of the variance:
$\sigma =\sqrt{46.4}\approx 6.81175$

Rounding the result to two decimal places gives 6.81.