1. TT 4302 N4 1 HB 1 Mathematics - Higher Module 1 - Statistics November 2004 Section B ( Non - calculator) Question 5 Question 5 scatter graphs and line of best fit Question 5X Question 5X stem and leaf diagram Question 6 Question 6 draw tree diagram and calculate combined probabilities Question 7 Question 7 grouped data, draw a histogram Question 8 Question 8 Calculate combined probabilities

2. TT 4302 N4 1 HB 2 5. Write down the type of correlation shown in each of the scatter graphs A and B Answer A is NegativeAnswer B is Zero Correlation The Marks for a group of pupils who sat two tests are shown in the Scatter graph below. 2 Marks Estimate the Test 1 mark for a pupil who scored 50 in Test 2. Show how you obtained your answer Answer about 60 2 Marks

3. TT 4302 N4 1 HB 3 5X. The number of letters received each day by a school is shown in the ordered stem – and - leaf diagram below. 0 6 6 7 8 12 2 2 4 7 8 2 0 3 7 7 9 Key 1 8 represents 18 letters On how many days did the school receive 6 letters?21 Mark What was the highest number of letters received?29 1 Mark Write down the mode121 Mark When the number of letters for another day is included in the data, the range increases by 1. How many letters did the school receive on that day? Write down 2 possible answers. Answer 5 or 30 2 Marks

4. TT 4302 N4 1 HB 4 6. Bob is taking penalties. The probability that Bob scores from the penalty spot is 3/5 for each penalty. Bob takes two penalties. Draw a fully labelled tree diagram showing all the probabilities. 1 st penalty 2 nd penalty Scores No score Scores No score Scores No score 3/5 2/5 3/5 2/5 3/5 2/5 3 Marks b) Calculate the probability that Bob scores exactly once on his two events ( 3/5 X 2/5 ) + ( 2/5 X 3/5 ) = 6/25 + 6/25 12/25 3 Marks

5. TT 4302 N4 1 HB 5 7. The table summarises the distances thrown in the discus event by 20 boys during a school sports day. Draw a histogram to represent the data. Distance, x (metres)Number of boys 0 < x ≤ 51 5 < x ≤ 100 10 < x ≤ 209 20 < x ≤ 305 30 < x ≤ 354 35 < x ≤ 401

6. TT 4302 N4 1 HB 6 3 Marks The distances thrown in the discus event by 20 girls are represented below

7. TT 4302 N4 1 HB 7 Write down 2 comparisons between the distances thrown by the boys and the girls Comparison 1 - Boys range greater than girls range Comparison 2 – Boys average greater than girls average. 2 Marks

8. TT 4302 N4 1 HB 8 8. A fair spinner has 4 equal sections. The sections are coloured red (R), white (W), blue (B) and yellow (Y). The arrow on the spinner is spun three times. Calculate the probability that the arrow lands on the same colour at least twice. RR and not R OR WW and not W OR BB and not B OR YY and not Y (¼ X ¼ X ¾) X 3 X 4 Also RRR OR WWW OR BBB OR YYY (¼ X ¼ X ¼) X 4 9/16 + 1/16 10/16 = 5/8 5 Marks