Question

Mark is interested in seeing how outgoing his residents are so he distributes a survey on extraversion to them. Mark is only interested in his own residents and is able to give surveys to all of them, so the data he collects represents a population.

x (extraversion score)

10

10

9

8

8

7

5

5

5

4

1) For the population Mark has data from, please calculate the following:

a) Mean:

b) Sum of Squares:

c) Variance:

d) Standard Deviation:

2) As you can see from the data, one of Mark’s residents received an extraversion score of 9. Please convert that resident’s score to a z-score (using the mean and standard deviation you found previously). What is the z-score for this resident?

3) Now we want to convert this resident’s score to a new distribution where the mean is 100 and the standard deviation is 10. What is this resident’s new raw score?

Answer 1

a)

mean =7.10\

b)sum of square =44.90

c)variance =4.99

d)Std deviaiton =2.23

2)

as z score =(X-mean)/std deviaiton

hence

S.No		X	z score
1		10.00	1.30
2		10.00	1.30
3		9.00	0.85
4		8.00	0.40
5		8.00	0.40
6		7.00	-0.04
7		5.00	-0.94
8		5.00	-0.94
9		5.00	-0.94
10		4.00	-1.39

3)

for new raw score =mean +z*std deviaion =100+z*10

S.No		X	z score	new raw score
1		10.00	1.30	113
2		10.00	1.30	113
3		9.00	0.85	108.5
4		8.00	0.40	104
5		8.00	0.40	104
6		7.00	-0.04	99.6
7		5.00	-0.94	90.6
8		5.00	-0.94	90.6
9		5.00	-0.94	90.6
10		4.00	-1.39	86.1