find the standard deviation for the group of data items. 10, 10, 12, 12, 14, 14 the standard deviation is…

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:

$1.79$