Week 2 - Central Tendency and Variance Assignment

Purpose: The purpose of this assignment is to work through an example of calculating measures of central tendency (mean, median, mode) and dispersion (variance and standard deviation). These basic statistics are the building blocks of subsequent course content.

Background: Review Chapters 3 & 4 in Essentials of Statistics for Criminology and Criminal Justice. Recall that to calculate variance, follow these steps:

1. Calculate the mean.
2. Then, for each value in the set of numbers subtract the mean and then square the result (hint: it helps to make a table of these numbers).
3. Lastly, work out the average of those squared differences.

Example:

Suppose you have these five values: 600, 470, 170, 430, and 300. The mean of these numbers is 394.

Value	Subtract from Mean	Squared
600	206	42436
470	76	5776
170	-224	50176
430	36	1296
300	-94	8836

The average of the squared values (the variance) is 21,704.

Instructions: At the end of this document is a data set consisting of exam scores for a set of students. Complete the table below using that data. Refer to your textbook for formulas and calculation content. Perform the calculations by hand.

Record your results in this document and submit as follows:

• Provide each answer in the table below under Results.
• Upload a separate file with your handwritten work showing how you reached your results.

Results

Statistic	Your Answer
Value of N
Mean
Median
Mode
Standard Deviation
Variance
Range

Data Set

Student	Exam Score
1	97
2	82
3	73
4	46
5	58
6	94
7	76
8	100
9	64
10	64
11	94
12	61
13	52
14	37
15	67
16	88
17	97
18	100
19	55
20	79
21	91
22	94
23	85
24	100
25	70
26	94
27	94
28	94
29	100
30	85
31	100
32	94
33	49
34	82
35	97
36	94
37	100
38	79
39	73
40	100
41	52
42	70