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.

Var

28

4

27

23

17

38

21

16

28

15

23

33

34

42

42

14

14

28

22

31

18

28

17

17

30

a.   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.

d.   Briefly summarize is a one paragraph description of the distribution.

Answer 1

28,4,27,23,17,38,21,16,28,15,23,33,34,42,42,14,14,28,22,31,18,28,17,17,30

Among the given 25 elements mean is sum of elelments / no of elements = 610/25 = 24.4

median is the middle element when we arrange in either increasing or decreasing order of elements

13 th element is median that is 23

Mode is the most repetitive element amont the elements which is 28.

Stem and Leaf Plot:

Stem Leaf

0 4

1 4 4 5 6 7 7 7 8

2 1 2 3 3 7 8 8 8 8

3 0 1 3 4 8

4 2 2

Basic Statistics:

Minimum:

4

Maximum:

42

Count:

25

Sum:

610

Mean:

24.4

Median:

23

Mode:

28

Standard Deviation:

9.403

Variance:

88.42

c) z = x - mean / sd = (46-24.4)/9.403 = 2.2971.

d) standard deviation is sqrt(variance) = 9.403