Question

You are the training coordinator for the IT department at the local community college. You are just completing a series of training workshops for the faculty that focused on how to develop online classes. The content of the sessions involved important concepts and principles of online instruction and instructional design as well as hands-on activities working in the course management system. You assessed their skills in using the program as you went along and are now interested in knowing if they acquired and retained the content knowledge. You develop an assessment with 50 multiple choice questions and administer it during the final training session.

Here are scores for the twenty faculty members who completed the assessment:

40	31	29	30	27
42	20	41	25	36
18	47	14	23	39
23	32	28	36	16

Using these results, complete the table below and then use your results to answer the questions that follow. (Please remember to round all answers to two decimal places: 0.00 at each step.) (23 points)

	X	X-M	(X-M)2
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
	?X=	? (X-M)=	?(X-M)2 =

1. What is the mean?

2. What is the mode(s)?

3. What is the median?

4. What is the range?

5. What is the variance?

6. What is the standard deviation?

Answer 1

putting above data into ascending order:

	X	X-M	(X-M)2
1	0	-27.85	775.6225
2	14	-13.85	191.8225
3	16	-11.85	140.4225
4	18	-9.85	97.0225
5	20	-7.85	61.6225
6	23	-4.85	23.5225
7	23	-4.85	23.5225
8	25	-2.85	8.1225
9	27	-0.85	0.7225
10	28	0.15	0.0225
11	29	1.15	1.3225
12	30	2.15	4.6225
13	31	3.15	9.9225
14	32	4.15	17.2225
15	36	8.15	66.4225
16	36	8.15	66.4225
17	39	11.15	124.3225
18	41	13.15	172.9225
19	42	14.15	200.2225
20	47	19.15	366.7225
total	557	0	2352.55

1)

mean = 557/20=27.85

2)

mode =23, 36 (as both appears twice)

3)

median =(n+1)/2 th value =10.5 th value =(28+29)/2 =28.5

4)

range =max-,min=47-0=47

5)

variance =(x-M)²/(n -1)=2352.55/(20-1)=123.8184

6)

std deviaiton =(123.8184)^1/2 =11.1274