Question

One hundred teachers attended a seminar on mathematical problem solving. The attitudes of representative sample of 12 of the teachers were measured before and after the seminar. A positive number for change in attitude indicates that a teacher's attitude toward math became more positive. The twelve change scores are as follows. 4; 8; −1; 1; 0; 4; −3; 2; −1; 5; 4; −2

1.) What is the standard deviation for this sample? (Round your answer to two decimal places.)

2.) What is the median change score? (Round your answer to one decimal place.)

*Please show step by step*

Answer 1

(1)

From the12 change scores, the following Table is calculated:

Sample Mean = is calculated as follows:

x	(x - )	(x - )2
4	2.25	5.0625
8	6.25	39.0625
- 1	- 2.75	7.5625
1	- 0.75	0.625
0	- 1.75	3.0625
4	2.25	5.0625
- 3	-4.75	22.5625
2	0.25	0.0625
- 1	- 2.75	7.5625
5	3.25	10.5625
4	2.25	5.0625
- 2	- 3.75	14.0625
Total =		120.25

Sample Variance (s²) is got as follows:

So,

Standard Deviation (s) is got as follows:

So,

Standard Deviation for this sample = 3.31

(b)

Arranging values in ascending ordr, we get:

- 3, - 2, - 1, - 1, 0, 1, 2, 4, 4,, 4, 5, 8

n = 12

Median is (12 + 1)/2th item = average of 6th & 7th item = (1 + 2)/2 = 1.5

So,

Media change score = 1.5