STATS question!

[tuckletoe]

Esme noted the test marks, x, of 16 people in a class. She found that Σ x = 824 and that the standard
deviation of x was 6.5.
(i) Calculate Σ(x − 50) and Σ(x − 50)^2

 

[Amna]

to find Σ(x − 50):
We know Σ(x)=824. and the total number of students is 16. So Σ(x − 50)= Σ(x) - (16 x 50) = 824 - 800 = 24.

to find Σ(x − 50)^2:
we know the formula for variance, so substitute the values in it. So you get (Σ(x − 50)^2)/16 - (Σ(x − 50) / 16)^2 = (6.5)^2
using simple algebra, we get Σ(x − 50)^2 = (42.25 + (24/16)^2) x 16 = 712.