Statistics and Probability [CIE Extended Mathematics 0580 (2017-2018)]

1	(2018/w/22/q18) 120 students choose what they want to do when they leave school. Their choice are shown in table. Choice Number of students University 57 Trainin 45 work 18 Complete the pie chart to show this information Label each sector clearly.......[4]
2	(2017/s/21/q16) Six students revise for a test. The scatter diagram shows the time, in hours, each student spent revising and their mark in the test. (a) The data for two more students is shown in table. Time(hours) 4.5 6.5 Mark 33 35 Plot these two points on the scatter diagram.....[1] (b) What type of correlation is shown on the scatter diagram.....[1] (c) Draw a line of best fit on the scatter diagram.....[1] (d) Another student spent 5.5 hours revising. Estimate a mark for this student....[1]
3	(2017/w/21/q) Ambers mean mark on five tests is 80. Her marks on four of these tests are 68, 81, 74 and 89 workout her mark on the fifth test......[2]
4	(2018/s/21/q18) The cumulative frequency diagram shows information about the time, m minutes, taken by 120 students to complete some homework. Use the cumulative frequency diagram to find an estimate of (a) the interquartile range, .......................................min [2] (b) the number of students who took more than 50 minutes to complete the homework. .............................................. [2]
5	(2018/s/21/q23) 40 people were asked how many times they visited the cinema in one month. The table shows the results Number of cinema visits 0 1 2 3 4 5 6 7 Frequency 5 5 6 6 7 3 6 2 a) (i) Find the mode. .............................................. [1] (ii) Calculate the mean. .............................................. [3] (b) Omar wants to show the information from the table in a pie chart. Calculate the sector angle for the people who visited the cinema 5 times. .............................................. [2]
6	(2018/w/21/q3) What type of correlation does the scatter diagram show? .................................................[1]
7	(2017/w/23/q21) The diagram shows the numbers of hummingbirds seen by Ali and Hussein in their gardens each day for 10 days. (a) Calculate the mean number of hummingbirds seen in Ali’s garden each day. ................................................. [3] (b) Work out the median number of hummingbirds seen in Hussein’s garden each day. ................................................. [2] (c) On one of these days there were 4 times as many hummingbirds seen in Hussein’s garden as in Ali’s garden. Which day was this? Day ................................................ [1]
8	(2017/w/21/22) Simon records the heights, h cm, of 200 sunflowers in his garden. The cumulative frequency diagram shows this information. (a) Find the number of these sunflowers that have a height of more than 160cm. ................................................... [2] (b) Sue records the heights, hcm, of 200 sunflowers in her garden. The cumulative frequency table shows this information. Height(h cm) Cumulative frquency h$\leq 100$ 0 h$\leq 110$ 20 h$\leq 120$ 48 h$\leq 130$ 100 h$\leq 140$ 140 h$\leq 150$ 172 h$\leq 160$ 188 h$\leq 170$ 200 On the grid above, draw another cumulative frequency diagram to show this information. [3] (c) Work out the difference between the median heights of Simon’s sunflowers and Sue’s sunflowers. ............................................. cm [2]
9	(2018/m/22/q1) "We eat more icecream as the temperature rises."  What type of correlation is this?....[1]
10	(2018/s/22/q13) 13 The histogram shows information about the time, t minutes, spent in a shop by each of 80 people Complete the frequency table. Time ($t$ minutes) $ 0 <t\leq 5$ $ 5 <t\leq 15$ $ 15 <t\leq 30$ $ 30 <t\leq 50$ $50 <t\leq 70$ Number of people 6 27 10 .........[2]
	to be continued

Answer Key

1. Figure
2. (a) \( (4.5,33),(6.5,35) \) (b) positive (c) Corrected ruled line (d) 33.5
3. 88
4. \( x-6, y--8 \)
5. (a) 27 (b) 3 (c) \( \frac{x-7}{3} \)
6. Negative
7. (a) 3.4 (b) 5 (c) \( \left|\mathrm{D}_{a y}\right| 10 \)
8. (a) 80 to 84 (b) Corrext curve or ruled lines (c) 26
9. Positive
10. 15 and 22

11. (a) 140000 (b) Points corredsly plotted at \( (40,80) \) and ( 80,150 ) (c) Correct ruled line of best fit (d) 80000 to 110000
12. (a) 25 (b) 12 (c) 5
13. (a) \( 71 < t \leqslant 72 \) (b) 72.3 or 72.27 to 72.28 (c) (i) \( 41,62,80,90 \) (c) (ii) Correct curve (c) (iii) 72.1 to 72.4 (c)(iv) 1.9 to 2.2 (d) 180
14. (a) \( 54,76,96 \) (b) 187 ce 186.8 to 186.9
15. (a) 1002 (b) \( 0.8,2.8,0.65 \) (c) \( 8,34,69 \), 136, 164 (d)Correct diagram (e) (i) 15 to 17 (e) (ii) 107 to 109 (e) (iii) 66 to 72
16. (a) 72.7 or 72.70 to 72.71 (b) (i) |23| 87200 345371 400| (ii) Correct graph (iii) (a) 69 to 70 (b) 20 to 23 (c) 72 to 75
17. (a) (i) 175.5 (ii) Fully correct histogram (b) (i) Fully correct cumulative frequency diagram (b)(ii)(a) 170 to 175 (b) 152 to 158
18. (a) (i) 280 (ii) 320 (iii) 90 (iv) 10 (b) (i) 250.2 (ii) Correct completion of histogram (c) \( |22 \mathrm{~m}| \) further