Answer :
Final answer:
To find the sum of squares of the observations with a given mean and standard deviation, we use the formula [tex]SS = n\(\sigma^2 + n(\mu)^2[/tex]. Substituting the given values, the sum of squares is 252500.
Explanation:
The question asks for the sum of squares of all the observations given the mean and standard deviation of the data. To find the sum of squares (SS), we can use the formula: [tex]SS = n\(\sigma^2 + n(\mu)^2[/tex], where n is the number of observations, \[tex]\sigma^2[/tex] is the variance (standard deviation squared), and [tex]\mu[/tex] is the mean. Given that the mean [tex]\mu[/tex] is 50, the standard deviation [tex](\(\sigma\))[/tex] is 5, and there are 100 observations, we substitute these values into the formula:
[tex]SS = 100\(\times\)5^2 + 100\(\times\)50^2 = 2500 + 250000 = 252500[/tex]
