Question

The following is a small data set of 25 observations. I want you to calculate some statistics by hand to cement the class material. You can use the regular formula for the variance or the computational formula - I’m just interested in the correct result. If you use the computational formula, you will want to calculate a separate row of each value squared in order to calculate the Sum(x^2). Excel can be used to solve this problem.

VarX
44
34
49
58
17
44
34
49
45
20
26
40
35
37
57
45
70
35
37
42
44
45
27
46
63

1. Create a Stem and Leaf Plot of the data (it is easy to do in Word by making a two column table and entering the numbers in there, bolding the stems)

b. Calculate the following (show your work):

• Mean
  • Median
  • Mode
  • Range
  • Variance
  • Std. Deviation
  • Coefficient of Variation

c. Calculate a z-score for a data value of 46. Describe this in words.

Answer 1

Ans. Data is in ascending order:-

Obs.	x	x2
1	17	289
2	20	400
3	26	676
4	27	729
5	34	1156
6	34	1156
7	35	1225
8	35	1225
9	37	1369
10	37	1369
11	40	1600
12	42	1764
13	44	1936
14	44	1936
15	44	1936
16	45	2025
17	45	2025
18	45	2025
19	46	2116
20	49	2401
21	49	2401
22	57	3249
23	58	3364
24	63	3969
25	70	4900
SUM =	1043	47241

• The value 46 is 0.34 standard deviation above the mean.