Question

Student scores on a chapter quiz are:

                6 3 4 9 7 5 5 2 10 9 8 4 4 7 6 3 2 10 9 5

a) Find the mean, median, mode and midrange for this data.

b) Find the range, standard deviation and variance for this data.

c) Find the z-score for the value 7 and the cutoffs for the data set that are considered unusual.

Answer 1

a)

b)

c)

Data which is beyond two standard deviations from mean is considered as unusual.

Table for z scores,

Data Points	Z score
6	0.039254170755643
3	-1.13837095191364
4	-0.745829244357213
9	1.21687929342493
7	0.431795878312071
5	-0.353287536800785
5	-0.353287536800785
2	-1.53091265947007
10	1.60942100098135
9	1.21687929342493
8	0.824337585868499
4	-0.745829244357213
4	-0.745829244357213
7	0.431795878312071
6	0.039254170755643
3	-1.13837095191364
2	-1.53091265947007
10	1.60942100098135
9	1.21687929342493
5	-0.353287536800785

Here all the values are in between -2 and 2. Hence all the datapoints are usual.

That is the data for which z score values are outside the interval (-2,2) are considered as unusual.