Answer:
[tex]\sigma^2=73.96 \ kg^2[/tex]
Step-by-step explanation:
Standard Deviation and Variance
If we have a data set of measured values the variance is defined as the average of the squared differences that each value has from the mean. The formula to calculate the variance is:
[tex]\displaystyle \sigma^2=\frac{\sum(x_i-\mu)^2}{n}[/tex]
Where [tex]\mu[/tex] is the mean of the measured values xi (i running from 1 to n), and n is the total number of values.
[tex]\displaystyle \mu=\frac{\sum x_i}{n}[/tex]
The standard deviation is known by the symbol [tex]\sigma[/tex] and is the square root of the variance. We know the standar deviation of the weight in kg of a group of teenagers to be 8.6 kg. Thus, the variance is
[tex]\sigma^2=8.6^2=73.96 \ kg^2[/tex]
[tex]\boxed{\sigma^2=73.96 \ kg^2}[/tex]
