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

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}=(\sum_(i=1)^(6)x_i)/(n)\\\\\Rightarrow\ \overline{x}=(30)/(6)=5`

The formula to find standard deviation:_

`\sqrt{\frac{\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{(14)/(6)}\approx1.53`