Statistics

The table shows the number of goals scored in 40 matches.

Number of goals	0	1	2	3	4	5
Frequency	3	7	11	9	6	4

Work out the mean number of goals per match.

45 fish are caught, tagged and released. Later 60 fish are caught and 9 of them are tagged. Estimate the number of fish in the lake and state one assumption.

From a cumulative frequency graph for 80 students' test marks, the lower quartile is 52, the median 61 and the upper quartile 69. (a) Find the interquartile range. (b) Compare with another class whose median is 64 and IQR is 9.

Two groups sat a test. Group A: minimum 40, lower quartile 55, median 63, upper quartile 71, maximum 90. Group B: minimum 35, lower quartile 49, median 66, upper quartile 70, maximum 82. Compare the distributions of the two groups.

A school has 84 students in the morning shift, 56 students in the evening shift. A stratified sample of 30 students is taken. How many should be from the morning shift?

The table shows times taken by commuters.

Time, t (minutes)	Frequency
0 < t ≤ 5	10
5 < t ≤ 10	25
10 < t ≤ 20	40
20 < t ≤ 40	30
40 < t ≤ 60	15

Calculate the frequency density for each class, ready to draw a histogram.