6 exam-style questions with full mark schemes and model answers. Write your own answer and the AI examiner marks it against the mark scheme.
The table shows the time, t minutes, that 30 customers waited to be served in a shop.
| Time (t minutes) | Frequency |
|---|---|
| 0≤t<10 | 5 |
| 10≤t<20 | 12 |
| 20≤t<30 | 9 |
| 30≤t<40 | 4 |
(a) Write down the modal class. (1 mark)
(b) Work out an estimate for the mean waiting time. (4 marks)
The histogram for a set of data has a class 20≤w<40 drawn with a frequency density of 3.5. Another class, 40≤w<50, contains 18 items of data.
(a) Work out the frequency of the class 20≤w<40. (2 marks)
(b) Work out the frequency density that should be used to draw the bar for the class 40≤w<50. (2 marks)
For two data sets of test marks, the box plots give the following summary values.
| Minimum | Lower quartile | Median | Upper quartile | Maximum | |
|---|---|---|---|---|---|
| Class A | 22 | 38 | 52 | 61 | 80 |
| Class B | 30 | 45 | 50 | 58 | 72 |
(a) Work out the interquartile range for Class A. (2 marks)
(b) Make one comparison of the marks of the two classes, referring to a specific statistic from the table. (2 marks)
Here are the numbers of goals scored by a netball team in each of 7 matches: 12,8,15,9,12,20,6.
(a) Work out the median number of goals. (2 marks)
(b) Work out the range. (1 mark)
A scatter graph plots the number of hours 10 students spent revising against their test score. The points show that students who revised for longer generally achieved higher scores.
(a) Describe the type of correlation shown. (1 mark)
(b) A teacher uses the line of best fit to predict the test score of a student who revised for 50 hours, even though the largest revision time in the data is 9 hours. Explain why this prediction may not be reliable. (1 mark)
Work out the mean of the following five numbers: 7,11,4,9,14. (1 mark)