Question 2:

Two samples have means of x₁= 100 and x₂= 110. The two samples are pooled into one large sample, for which the mean x is calculated. What is x if the two sample sizes are:

a) n₁= 30, n₂= 70

b) n₁= 50, n₂= 50

Question 3:

A Quantitative Methods course has historically boasted of an excellent performance. The module is also known to have a high attendance at tutorials and lectures. The following is the attendance of a sample of 20 students at tutorials. The figures show the number of times that each of these students were present over the 12-week period of the academic term.

10	12	8	11	9	7	2	8	9	11
1	10	8	4	10	5	11	9	9	6

1. Estimate the average student attendance for this given data.

1. Calculate the median attendance and explain how the median figure obtained can be compared to the average in (i) above.

1. Calculate variance and standard deviation for the given data

Question 4:

The number of students that sat the end of year exam is given as grouped data categorised by performance.

Performance Group	Number of Students
Above 90%	3
80% - 90%	5
70% - 80%	5
60% - 70%	6
50% - 60%	5
40% - 50%	3
30% - 40%	2
20% - 30%	1

1. What is the mean performance of the grouped data above?
2. Showing your steps, calculate the standard deviation of this grouped data and discuss the meaning of this statistic in the context of the data.

Exam-type questions:

Question 1:

a) A factory employs staff in four departments for which the average (mean) wage per employee per week is as follows:

Department	W	X	Y	Z
Mean wage	50	100	70	80
Number of employees	20	5	10	5

Calculate average (mean) wage per employee per week

b) Calculate the median of the scores 34, 23, 78, 12, 56, 43, 28, 9, 24 and 87

c) Calculate range, variance and standard deviation for the following data set:

3, 5, 8, 11, 13

d) Discuss advantages and disadvantages of the mean, median and the mode

e) Discuss advantage and disadvantages of standard deviation and range.