Question

A population of N = 15 scores has a mean of μ = 8. One score in the population is changed from X = 20 to X = 5. What is the value for the new population mean?

A sample of n = 9 scores has a mean of M = 20. One of the scores is changed and the new mean is found to be M = 22. If the changed score was originally X = 7, what is its new value?

Calculate SS, variance, and standard deviation for the following sample of n = 8 scores: 0, 4, 1, 3, 2, 1, 1, 0.

Answer 1

A). If µ=8 and N=15,

the sum of the scores was 8*15 = 120
Now, one of the scores was changed.

It was originally included at 20 but it is corrected to 5.
120 - 20 + 5 = 105
Now in this problem N does not change.
105/15 = 7
The new population mean is 7

B)

9 * 20 = 180
9 *22 = 198

198 - 180 = 18
If the original score was 7, then the new score would be

7 + 18 => 25

C)

We have 8 scores: 0,4,1,3,2,1,1,0

Even though you haven't been asked for it,.

we need to calculate the mean.

=(0+4+1+3+2+1+1+0)/8

=12/8

=3/2

=1.5

Next, let's calculate the SS (sum of the squares)

For each score the square of the difference between the score and the mean score is:

(0-1.5)² = 2.25

(4-1.5)² = 6.25

(1-1.5)² = 0.25

(3-1.5)² = 2.25

(2-1.5)²= 0.25

(1-1.5)²= 0.25
(1-1.5)²= 0.25
(0-1.5)² = 2.25

Now add them to get the SS

2.25+6.25+0.25+2.25+0.25+0.25+0.25+2.25 = 14.00 = SS

Variance = SS/(n-1) = 14/(8-1) = 14/7= 2

Standard deviation = √variance = √2=1.414