Question

Find the standard deviation for the group of data items 4, 4, 4, 4, 6, 8 The standard deviation is (Simplify your answer. Round to two decimal places as needed.)

Answer 1

Answer: 1.53

Step-by-step explanation:

The given data : 4, 4, 4, 4, 6, 8

Number of data values : n= 6

The mean value of the given data will be  :-

$\overline{x}=\dfrac{\sum_{i=1}^{6}x_i}{n}\\\\\Rightarrow\ \overline{x}=\dfrac{30}{6}=5$

The formula to find standard deviation:_

$\sqrt{\dfrac{\sum(x-\overline{x})^2}{n}]$

Now,

$\sum_{i=1}^{6}(x_i-\overline{x})^2=(-1)^2+(-1)^2+(-1)^2+(-1)^2+(1)^2+(3)^2\\\\=1+1+1+1+1+9=14$

The standard deviation will be :-

$\sigma=\sqrt{\dfrac{14}{6}}\approx1.53$