| Date | May 2012 | Marks available | 1 | Reference code | 12M.2.sl.TZ2.3 |
| Level | SL only | Paper | 2 | Time zone | TZ2 |
| Command term | State | Question number | 3 | Adapted from | N/A |
Question
200 people were asked the amount of time T (minutes) they had spent in the supermarket. The results are represented in the table below.
State if the data is discrete or continuous.
State the modal group.
Write down the midpoint of the interval 10 < T ≤ 20 .
Use your graphic display calculator to find an estimate for
(i) the mean;
(ii) the standard deviation.
The results are represented in the cumulative frequency table below, with upper class boundaries of 10, 20, 30, 40, 50.
Write down the value of
(i) q;
(ii) r.
The results are represented in the cumulative frequency table below, with upper class boundaries of 10, 20, 30, 40, 50.
On graph paper, draw a cumulative frequency graph, using a scale of 2 cm to represent 10 minutes (T) on the horizontal axis and 1 cm to represent 10 people on the vertical axis.
Use your graph from part (f) to estimate
(i) the median;
(ii) the 90th percentile of the results;
(iii) the number of people who shopped at the supermarket for more than 15 minutes.
Markscheme
continuous (A1)
[1 mark]
20 < T ≤ 30 (A1)
[1 mark]
15 (A1)
[1 mark]
(i) 21.5 (G2)
(ii) 9.21 (9.20597…) (G1)
[3 marks]
(i) q = 194 (A1)
(ii) r = 200 (A1)
[2 marks]
(A1)(A2)(ft)(A1)
Notes: Award (A1) for scale and axis labels, (A2)(ft) for 5 correct points, (A1)(ft) for 4 or 3 correct points, (A0) for less than 3 correct points, (A1) for smooth curve through their points, starting at (0, 0). Follow through from their answers to parts (e)(i) and (e)(ii).
[4 marks]
(i) 22.5 ± 2 (A1)
(ii) 32 ± 2 (M1)(A1)(ft)(G2)
Note: Award (M1) for lines drawn on graph or some indication of method, follow through from their graph if working is shown.
(iii) 44 ± 2 (A1)(ft)
Note: Follow through from their graph if working is shown.
200 − 44 = 156 (M1)(A1)(ft)(G2)
Note: Award (M1) for subtraction from 200, follow through from their graph if working is shown.
[6 marks]
Examiners report
(a) Many candidates thought that this was discrete data.
(b) This part was very well done with the occasional candidate writing down the number rather than the group.
(c) Fairly well done although 15.5 was seen quite often.
(d) This was really badly done with most candidates only putting the midpoints into their GDC or only putting the frequencies into their GDC. Perhaps they did not know how to use their GDC correctly.
(e) The values of q and r were mostly correct.
(f) Most candidates plotted the points correctly. Some had problems plotting the 23 and 173. A few candidates used the midpoints instead of the end points and some drew bar charts.
(g) There was a lot of follow through marks gained here by those candidates who drew lines or put marks on their graphs in the correct places.
