Respuesta :
Variance is average of squared error of observations from mean. The variance of given data is 5.2
How to calculate variance of a given data set?
Variance is average of squared error of observations from mean.
- If the data set is composed of n elements,
- its ith element is [tex]x_i[/tex] ,
- and mean of the data set is [tex]\overline{x}[/tex] ,
then its variance is given as:
[tex]\sigma^2 = \dfrac{1}{n} \sum_{i=1}^n(x_i-\overline{x})^2[/tex]
The given data set is 4,7,4,10,5
Thus, n = 5 (total 5 observations (data values) )
Their mean is [tex]\overline{x} = 6[/tex] (it is taken as 'm', but for ease with formula, take it as [tex]\overline{x}[/tex] )
Thus, their variance is calculated as:
[tex]\sigma^2 = \dfrac{1}{n} \sum_{i=1}^n(x_i-\overline{x})^2 \\\\\sigma^2 = \dfrac{(4-6)^2 + (7-6)^2 + (4-6)^2 + (10-6)^2 +(5 - 6)^2}{5} \\\\\sigma^2 = \dfrac{4 + 1 + 4 + 16 + 1}{5} = \dfrac{26}{5} = 5.2[/tex]
Thus,
The variance of given data is 5.2
Learn more about variance here:
https://brainly.com/question/3699980
