Question

What is the standard deviation of the following data set rounded to the nearest tenth?

7.7, 8.4, 9, 8, 6.9

Answer 1

0.78422, so the nearest tenth being 0.8. Have a good day!

Answer 2

The standard deviation of the data is 0.7.

Explanation:

Given : Data 7.7, 8.4, 9, 8, 6.9

To find : What is the standard deviation of the following data set rounded to the nearest tenth?

Solution :

We can apply the standard deviation formula,

`\sigma^2= \frac{(x_1-\overline{x})^2+(x_2-\overline{x})^2+...+(x_n-\overline{x})^2}{n}`

Where,
`\overline{x}` is the arithmetic mean

First we find the arithmetic mean

`\overline{x}=(\sum x_i)/(n)`

`\overline{x}=(7.7+8.4+ 9+ 8+6.9)/(5)`

`\overline{x}=(40)/(5)`

`\overline{x}=8`

Now, substitute the values in the standard deviation formula,

`\sigma^2= \frac{(x_1-\overline{x})^2+(x_2-\overline{x})^2+...+(x_n-\overline{x})^2}{n}`

`\sigma^2= ((7.7-8)^2+(8.4-8)^2+(9-8)^2+(8-8)^2+(6.9-8)^2)/(5)`

`\sigma^2=((-0.3)^2+(0.4)^2+(1)^2+(0)^2+(-1.1)^2)/(5)`

`\sigma^2=(0.09+ 0.016+ 1+0+1.21)/(5)`

`\sigma^2=(2.316)/(5)`

`\sigma^2=0.4632`

`\sigma=√(0.4632)`

`\sigma=0.680`

Therefore, The standard deviation of the data is 0.7.