Question

The following set of data is from a sample of n = 7: 17 7 4 9 0 7 3

a.Compute the mean,median and mode.

b.Compute the range,variance,standard deviation and coefficient of variation.

c.compute the z scores, are there any outliers?

d.Describe the shape of the data set.

Answer 1

Following table shows the ordered data set and calculations for mean, median and mode:

S.No.	X	(X-mean)^2
1	0	45.0241
2	3	13.7641
3	4	7.3441
4	7	0.0841
5	7	0.0841
6	9	5.2441
7	17	105.8841
Total	47	177.4287

(a)

The mean is

The median: There are 7 data values so median will be 4th data value. That is median is 7.

Mode: Mode is the data value with highest frequency. So mode is 7.

(b)

Range = Maximum - minimum = 17 -0 = 17

Variance:

Standard deviation:

(c)

The formula for z-score is

Following table shows all the z-scores:

X	z-score
0	-1.23
3	-0.68
4	-0.5
7	0.05
7	0.05
9	0.42
17	1.89

Since no z-scores are outside -2 and 2 so there are no outliers.

d)

It seems that distribution is symmetric. It is not skewed to right or left.