The mean of the set of numbers 2,3,(k+1),(k+3) and 17 is (k+l). calculate the standard deviation

The set of numbers is $2, 3, (k+1), (k+3), 17$. There are 5 numbers.
The mean of these numbers is $(k+1)$.
The formula for the mean is $\text{Mean} = \frac{\sum x}{N}$.

Multiply both sides by 5:

Subtract $2k$ from both sides:

Subtract 5 from both sides:

Substitute $k=7$ into the expressions:
$k+1 = 7+1 = 8$
$k+3 = 7+3 = 10$
The set of numbers is $2, 3, 8, 10, 17$.
The mean of the set is $k+1 = 7+1 = 8$.

The mean $\mu = 8$.
For $x_1 = 2$: $(2-8)^2 = (-6)^2 = 36$
For $x_2 = 3$: $(3-8)^2 = (-5)^2 = 25$
For $x_3 = 8$: $(8-8)^2 = (0)^2 = 0$
For $x_4 = 10$: $(10-8)^2 = (2)^2 = 4$
For $x_5 = 17$: $(17-8)^2 = (9)^2 = 81$

The formula for the population standard deviation ($\sigma$) is $\sigma = \sqrt{\frac{\sum (x_i - \mu)^2}{N}}$.
Here, $N=5$ (the number of values).

The standard deviation is 5.4037.