Question

find the standard deviation for the group of data items. 10, 10, 12, 12, 14, 14 the standard deviation is. (simplify your answer. round to two decimal places as needed.)

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{10 + 10+12 + 12+14 + 14}{6}=\frac{72}{6}=12$.

Step2: Calculate the squared - differences

For $x = 10$: $(10 - 12)^2=(-2)^2 = 4$. Since there are 2 values of 10, the total contribution is $2\times4 = 8$.
For $x = 12$: $(12 - 12)^2=0^2 = 0$. Since there are 2 values of 12, the total contribution is $2\times0 = 0$.
For $x = 14$: $(14 - 12)^2=2^2 = 4$. Since there are 2 values of 14, the total contribution is $2\times4 = 8$.
The sum of squared - differences $\sum(x-\bar{x})^2=8 + 0+8=16$.

Step3: Calculate the variance

The variance $s^2=\frac{\sum(x - \bar{x})^2}{n-1}$, where $n = 6$. So $s^2=\frac{16}{6 - 1}=\frac{16}{5}=3.2$.

Step4: Calculate the standard deviation

The standard deviation $s=\sqrt{s^2}=\sqrt{3.2}\approx1.79$.

Answer:

$1.79$