Noesis
Level 2 — RecallBasic Data & Probability

Basic Data & Probability

⏱ 30 minutes40 marksprintable — key stays hidden on paper

Level: 2 (Recall & Standard Problems) Time limit: 30 minutes Total marks: 40

Answer all questions. Use ...... for any working shown.

Q1. Define the difference between primary data and secondary data, giving one example of each. (4 marks)

Q2. The tally chart below shows favourite fruits of a class.

Fruit Tally
Apple
Banana
Cherry
Mango

Copy and complete a frequency table, and state the total number of students. (4 marks)

Q3. A pie chart shows how 60 students travel to school. The "Walk" sector has an angle of 120°120°. (a) How many students walk? (2 marks) (b) If 15 students cycle, what angle represents "Cycle"? (2 marks)

Q4. Find the mean, median, mode and range of the following data set: (6 marks) 7, 4, 9, 4, 6, 10, 4, 127,\ 4,\ 9,\ 4,\ 6,\ 10,\ 4,\ 12

Q5. The table shows the number of goals scored in 20 matches. (4 marks)

Goals 0 1 2 3 4
Frequency 3 6 5 4 2

Calculate the mean number of goals per match.

Q6. Estimate the mean of the grouped data below using midpoints. (5 marks)

Height (cm) Frequency
10≤h<2010 \le h < 20 4
20≤h<3020 \le h < 30 7
30≤h<4030 \le h < 40 9

Q7. A fair six-sided die is rolled once. (a) Write the sample space. (1 mark) (b) Find the probability of rolling an even number. (2 marks) (c) Find the probability of rolling a number greater than 4. (2 marks)

Q8. The probability that it rains tomorrow is 0.350.35. Find the probability that it does not rain. State the rule you used. (3 marks)

Q9. A bag contains 5 red, 3 blue and 2 green marbles. One marble is drawn at random. Find: (a) P(red)P(\text{red}) (1 mark) (b) P(not blue)P(\text{not blue}) (2 marks)

End of paper

Answer keyMark scheme & solutions

Q1. (4 marks)

  • Primary data: data collected first-hand by the investigator for their own purpose. (1) Example: results of a survey you conducted / measuring heights yourself. (1)
  • Secondary data: data collected by someone else / already existing, used for a new purpose. (1) Example: population figures from a census / data from a textbook or website. (1) Why: distinction rests on who collected it and for what purpose.

Q2. (4 marks) Counting tallies:

Fruit Frequency
Apple 8
Banana 5
Cherry 3
Mango 9

(1 each correct row, allow 3 for any one slip) Total =8+5+3+9=25= 8+5+3+9 = 25 students. (implicit in marks; total must be stated)

Q3. (4 marks) (a) Full circle =360°=360° represents 60 students, so each student =6°=6°. Walk =120360×60=20=\dfrac{120}{360}\times 60 = 20 students. (1 method, 1 answer) (b) Cycle angle =1560×360=90°=\dfrac{15}{60}\times 360 = 90°. (1 method, 1 answer)

Q4. (6 marks) Data: 7,4,9,4,6,10,4,127,4,9,4,6,10,4,12 (n=8n=8).

  • Mean =7+4+9+4+6+10+4+128=568=7=\dfrac{7+4+9+4+6+10+4+12}{8}=\dfrac{56}{8}=7. (1 sum, 1 answer)
  • Ordered: 4,4,4,6,7,9,10,124,4,4,6,7,9,10,12. Median =6+72=6.5=\dfrac{6+7}{2}=6.5 (mean of 4th & 5th values). (1 order, 1 answer)
  • Mode =4=4 (appears three times). (1)
  • Range =12−4=8=12-4=8. (1)

Q5. (4 marks) ∑fx=(0)(3)+(1)(6)+(2)(5)+(3)(4)+(4)(2)=0+6+10+12+8=36\sum fx = (0)(3)+(1)(6)+(2)(5)+(3)(4)+(4)(2)=0+6+10+12+8=36. (2) ∑f=20\sum f = 20. Mean =3620=1.8=\dfrac{36}{20}=1.8 goals. (2)

Q6. (5 marks) Midpoints: 15, 25, 35. ∑fx=4(15)+7(25)+9(35)=60+175+315=550\sum fx = 4(15)+7(25)+9(35)=60+175+315=550. (2) ∑f=4+7+9=20\sum f = 4+7+9=20. (1) Estimated mean =55020=27.5=\dfrac{550}{20}=27.5 cm. (2) Why estimate: exact values within groups unknown, midpoint represents each class.

Q7. (5 marks) (a) Sample space ={1,2,3,4,5,6}=\{1,2,3,4,5,6\}. (1) (b) Even numbers {2,4,6}\{2,4,6\}: P=36=12P=\dfrac{3}{6}=\dfrac12. (1,1) (c) Greater than 4 {5,6}\{5,6\}: P=26=13P=\dfrac{2}{6}=\dfrac13. (1,1)

Q8. (3 marks) Complementary events: P(A′)=1−P(A)P(A')=1-P(A). (1 rule) P(no rain)=1−0.35=0.65P(\text{no rain})=1-0.35=0.65. (2)

Q9. (3 marks) Total marbles =5+3+2=10=5+3+2=10. (a) P(red)=510=12P(\text{red})=\dfrac{5}{10}=\dfrac12. (1) (b) P(not blue)=1−310=710P(\text{not blue})=1-\dfrac{3}{10}=\dfrac{7}{10}. (1 method, 1 answer)

[
{"claim":"Q4 mean is 7","code":"data=[7,4,9,4,6,10,4,12]\nresult = (sum(data)/len(data))==7"},
{"claim":"Q4 median is 6.5 and range is 8","code":"data=sorted([7,4,9,4,6,10,4,12])\nmed=(data[3]+data[4])/2\nrng=data[-1]-data[0]\nresult = (med==6.5) and (rng==8)"},
{"claim":"Q5 mean goals is 1.8","code":"fx=0*3+1*6+2*5+3*4+4*2\nresult = Rational(fx,20)==Rational(18,10)"},
{"claim":"Q6 grouped mean estimate is 27.5","code":"fx=4*15+7*25+9*35\nresult = Rational(fx,20)==Rational(55,2)"},
{"claim":"Q8 complement 0.65","code":"result = (1-Rational(35,100))==Rational(65,100)"},
{"claim":"Q9b P(not blue)=7/10","code":"result = (1-Rational(3,10))==Rational(7,10)"}
]