Scatter Diagrams SAMs 1 Numeracy Unit 1 Q6

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1 Scatter Diagrams SAMs 1 Numeracy Unit 1 Q6 6. Nerys takes her cousins, Ben, Elwyn and Denny to an aquarium in North Wales. a) Denny records estimates for the length and width of some of the fish he sees in the aquarium. width length He draws a scatter diagram as shown below. Length in cm Width in cm i) One of the fish is 4cm wide. Write down its length. [1].. ii) Another fish is 14cm long. Write down its width. [1].. iii) The width of a yellow fish is exactly the same as its length. Indicate on the scatter diagram which point represents the yellow fish. [1]

2 SAMS 1 NUMERACY UNIT 1 Q9b 9b) Before agreeing to improve the hotel s swimming pool, the manager of the Hafod Hotel decides to check the price of a double room for a night, in hotels with and without swimming pools.. She has grouped her results, 120 hotels with a swimming pool and 120 hotels without a swimming pool. Prices for double rooms at hotels with a swimming pool Cumulative frequency Price ( s)

3 Prices for double rooms at hotels without a swimming pool. Cumulative frequency. Price ( s) (i) The Hafod Hotel owners look at the manager s findings and ask: How many more hotels have double rooms that are priced at more than 140 per night in hotels with swimming pools than in hotels without swimming pools? What response should the manager give? You must show all your working. [2].... ii) To help decide whether or not to improve the Hafod Hotel s swimming pool, the manager s findings need to be interpreted. Describe the difference in the distribution of prices for a double room in hotels with a swimming pool compared with those without a swimming pool. You must use an appropriate average and measure of spread and interpret your findings. [4]

4 .... SAMs 1 Numeracy Unit 1 Q The box-and-whisker plot shows information about the height, in feet, of waves measured at a beach on a particular day. Height (feet) (a) About what fraction of the waves measured were less than 6 feet? [1].. (b) Circle either TRUE or FALSE for each of the following statements. [2] The smallest wave measured was 5 feet. TRUE FALSE The range of the heights of the waves measured was 6 5 feet. Approximately a half of the waves measured were more than 9 5 feet. Approximately a quarter of the waves measured were between 6 feet and 9 5 feet. TRUE TRUE TRUE FALSE FALSE FALSE

5 The biggest wave measured was feet. TRUE FALSE SAMs 2 Numeracy Unit 1 Q5 5. Billy and Shaun both completed a survey. They collected leaves from a number of trees and decided to measure them. They agreed on the following decisions. The length of the leaf does not include the stem The width of the leaf is measured at the widest section of the leaf. a) Why have they both agreed on these decisions about measuring the leaves. [1]. b) Billy measured the length and width of each leaf he had collected. Shaun did the same with his leaves. They displayed the lengths and widths of their own leaves on separate diagrams. Billy s and Shaun s scatter diagram are shown below.

6 Length in cm Billy s scatter diagram Width in cm Length in cm Shaun s scatter diagram

7 Width in cm i) Who found the longest leaf? Write down the length of this leaf..cm [1] ii) Only one of the two boys collected all his leaves from the same tree. Who was this Billy or Shaun? Give a reason for your answer. [1].. iii) Draw, by eye, a line of best fit on Shaun s scatter diagram. [1] iv) Shaun realises he has one more leaf that he has not included on his scatter diagram. The leaf is damaged in such a way that Shaun cannot measure its width. The length of the leaf is 8.5cm. Write down a reasonable estimate for the width of this leaf. Width =.cm [1]

8 SAMs 2 Numeracy Unit 1 Q13 13.The information shown below was found in a holiday brochure for a small island. Rainfall in cm The information shows monthly data about the rainfall in centimetres. (a) Looking at the rainfall, which month had the most changeable weather? You must give a reason for your answer. [1]

9 (c) In July 2014, the interquartile range for the rainfall was 10 cm and the range was 40cm. Is it possible to say whether July has more or less rainfall than June? You must give a reason for your answer. [1] SAMs 2 Numeracy Unit 2 Q12 12.In Aberfar, a group of local people took part in a challenge to learn how to tie a Celtic knot. The frequency diagram shows the times taken by the local people to tie a Celtic knot for the first time.

10 (a) Complete the cumulative frequency table for the times taken by the local people to tie a Celtic knot for the first time. [2] (b) The graph paper opposite shows a cumulative frequency diagram of the times taken by 140 visitors to Wales to tie a Celtic knot for the first time. On the same graph, draw a cumulative frequency diagram for the times taken by the local people to tie a Celtic knot for the first time. [2] (c) The visitors had been set a target that 100 of the group would finish within 17 minutes. By how many minutes did they miss or beat their target? [2]

11 Did they miss the target or beat the target?.. By how many minutes? WJEC NUMERACY NOV 2016 UNIT 1 Q5b.c 5b)Rowena states a hypothesis Boys do better than girls in their English tests She displays the test marks for 5 girls and 5 boys in scatter diagrams Mark in Welsh Girls test results Mark in English

12 Mark in Welsh Boys test results Mark in English i) Does the data support Rowena s hypothesis? You must give reason for your answer. [1].. ii) How could Rowena improve the testing of her hypothesis? [1].. c) Draw, by eye, a line of best fit to estimate how many marks you might expect a boy to score in a Welsh test if he scored 50 marks in his English test? [1 ].. WJEC NUMERACY NOV 2016 UNIT 1 Q girls were asked how long they spent revising for their GCSE examinations. The cumulative frequency diagram shows the results.

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14 b) 140 boys were asked how long they spent revising for their GCSE examinations. The cumulative frequency diagram shows the results.

15 WJEC Numeracy Nov 2016 Unit 1 Q13

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17 WJEC Numeracy Summer 2017 Unit 1 Q Time (seconds)

18 WJEC Numeracy Summer 2017 Unit 1 Q11

19 WJEC Numeracy Summer 2017 Unit 2 Q4

20 Mass (kg) Height (cm)

21 .. (d) Do you think this is a fair dice? You must give a reason for your choice. [1].... WJEC AOM Unit 2 June 15 Q8 8. Every Monday for 6 weeks, the number of customers entering a juice bar and the takings of the juice bar were recorded The takings were recorded correct to the nearest 10 The table below shows the results. Number of customers Takings

22 a) 0n the graph paper below draw a scatter diagram of these results. [2] Takings Number of customers b) Draw, by eye, a line of best fit on your scatter diagram. [1] c) Estimate the takings for a Monday when there are 95 customers. [1]... d) Approximately how much does a customer spend, on average, in the juice bar on a Monday? [2] WJEC AOM Unit 2 June 14 Q11

23 11. The manager of a tea shop at a castle kept some records every day for 7 days. The manager recorded The number of visitors to the castle The total money taken at the tea shop. Day Number of visitors to the castle Monday Tuesday Wednesday Thursday Friday Saturday Sunday Tea shop takings( ) a) On the graph paper provided, draw a scatter diagram of these results. [3] Tea shop takings Number of visitors to the castle b)draw, by eye, a line of best fit on your scatter diagram [1]

24 d) Describe the correlation between the number of visitors to the castle and the tea shop takings. [1].. e) The manager of the tea- shop states. My records tell me that each visitor to the castle spends more than 1 each at the tea-shop i) Explain why the manager might have come to this conclusion. [2].... ii) The statement is not necessarily true. Explain why the statement may not be true. [1].... WJEC AOM Unit 2 Jan 14 Q9 9. Bethany and Michelle have both completed a project about pets. They weighed and measured the heights of a number of pets. They each drew a scatter diagram showing their results. Bethany s Scatter Graph Michelle s Scatter Graph Height Height Weight Weight

25 a) One of the girls scatter diagrams shows weights and heights of pet cats, dogs and hamsters. The other girl s scatter diagram shows weights and heights of only pet cats. Which of the girls, Bethany or Michelle, considered only pet cats. Give a reason for your answer. [1] b) Draw line of best fit, by eye, on Michelle s scatter diagram. [1]