Question

What is the sum of squares for the following sample of 5 scores: 5, 4, 3, 9, 4?

A. 5

B. 15

C. 20

D. 22

Answer 1

From given 5 scores we get, sample mean is,

$\bar x =\frac { 5 + 4+3+9+4}{5}= \frac { 25}{5}= 5$

We want to find, the sum of squares $\sum ( x -\bar x)^2$

$\sum ( x -\bar x)^2 =( 5 -5)^2 + ( 4 -5)^2 +( 3 -5)^2 +( 9 -5)^2 +( 4 -5)^2$

$\sum ( x -\bar x)^2 =0 + ( -1)^2 +( -2)^2 +( 4)^2 +( -1)^2$

$\sum ( x -\bar x)^2 =0 + 1 +4 +16 +1$

$\sum ( x -\bar x)^2 = 22$

The sum of squares is 22

Answer: D) 22