find the standard deviation for the group of data items. 15, 15, 15, 17, 19, 19, 19\nthe standard deviation…

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{15\times3 + 17+19\times3}{3 + 1+3}=\frac{45+17 + 57}{7}=\frac{119}{7}=17$.

Step2: Calculate the squared - differences

For $x_1 = 15$, $(x_1-\bar{x})^2=(15 - 17)^2=4$. Since there are 3 values of 15, the sum of squared - differences for 15 is $3\times4 = 12$. For $x_2 = 17$, $(x_2-\bar{x})^2=(17 - 17)^2=0$. For $x_3 = 19$, $(x_3-\bar{x})^2=(19 - 17)^2=4$. Since there are 3 values of 19, the sum of squared - differences for 19 is $3\times4 = 12$. The sum of squared - differences $\sum(x_i-\bar{x})^2=12+0 + 12=24$.

Step3: Calculate the variance

The variance $s^2=\frac{\sum(x_i-\bar{x})^2}{n - 1}$, where $n = 7$. So $s^2=\frac{24}{7 - 1}=\frac{24}{6}=4$.

Step4: Calculate the standard deviation

The standard deviation $s=\sqrt{s^2}=\sqrt{4}=2.00$.

Answer:

$2.00$