Question

1. Calculate standard deviation for the following population of N = 6 scores: 5, 0, 9, 3, 8, 5. Use the computational formula and show your work. (Hint: You should get the same answer for this question that you got for question #2).

For the following sample, use the computational formula to calculate SS and then compute the sample variance and standard deviation. Scores: 1, 4, 2, 1​

A distribution of scores has a mean of M = 42. If the standard deviation is SD = 2, would a score of X = 48 be considered an extreme value?

Answer 1

1) For the given sample 5, 0, 9, 3, 8, 5. to find the population standard deviation we need to find the mean first as:

Mean = (5 + 0 + 9 + 3 + 8 + 5)/6
= 30/6
Mean = 5

The standard deviation for mean is calculated as:

σ =√(1/6 ) x ((5 - 5)² + ( 0 - 5)² + ( 9 - 5)² + ( 3 - 5)² + ( 8 - 5)² + ( 5 - 5)²)
= √(1/6) x ((0)² + (-5)² + (4)² + (-2)² + (3)² + (0)²)
= √(1/6) x ((0) + (25) + (16) + (4) + (9) + (0))
= √(1/6) x (54)
= √(9)
= 3

2) The SS ( Sum of squares) for the values 1, 4, 2, 1​ is calculated as:

SS=(1²+4²+2²+1²)-(8²)/4

Where Xi is the values and N is no of values which is 4.

SS=6

Sample variance is calculated as:

=> S²= SS/N-1

=> 6/(4-1)

=>2

Standard deviation=√S²

Sd= √2

=> 1.414

c) The given distribution of scores has a mean of M = 42. If the standard deviation is SD = 2, to find a score of X = 48 is an extreme or typical we need to find the Z score which is calculated as:

any score which is having Z score more than 3 or less -3 that value is an extreme value hence the value X=48 is an extreme value.