Respuesta :
Answer:
The standard deviation of the data is 0.7.
Step-by-step 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,
[tex]\sigma^2= \frac{(x_1-\overline{x})^2+(x_2-\overline{x})^2+...+(x_n-\overline{x})^2}{n}[/tex]
Where, [tex]\overline{x}[/tex] is the arithmetic mean
First we find the arithmetic mean
[tex]\overline{x}=\frac{\sum x_i}{n}[/tex]
[tex]\overline{x}=\frac{7.7+8.4+ 9+ 8+6.9}{5}[/tex]
[tex]\overline{x}=\frac{40}{5}[/tex]
[tex]\overline{x}=8[/tex]
Now, substitute the values in the standard deviation formula,
[tex]\sigma^2= \frac{(x_1-\overline{x})^2+(x_2-\overline{x})^2+...+(x_n-\overline{x})^2}{n}[/tex]
[tex]\sigma^2= \frac{(7.7-8)^2+(8.4-8)^2+(9-8)^2+(8-8)^2+(6.9-8)^2}{5}[/tex]
[tex]\sigma^2=\frac{(-0.3)^2+(0.4)^2+(1)^2+(0)^2+(-1.1)^2}{5}[/tex]
[tex]\sigma^2=\frac{0.09+ 0.016+ 1+0+1.21}{5}[/tex]
[tex]\sigma^2=\frac{2.316}{5}[/tex]
[tex]\sigma^2=0.4632[/tex]
[tex]\sigma=\sqrt{0.4632}[/tex]
[tex]\sigma=0.680[/tex]
Therefore, The standard deviation of the data is 0.7.
