Noesis
Level 1 — RecognitionBasic Data & Probability

Basic Data & Probability

⏱ 20 minutes30 marksprintable — key stays hidden on paper

Level: 1 (Recognition) Time limit: 20 minutes Total marks: 30

Section A — Multiple Choice (1 mark each)

Choose the ONE correct answer.

Q1. Data that you collect yourself directly, for the first time, is called:

  • A) Secondary data
  • B) Primary data
  • C) Grouped data
  • D) Tallied data

Q2. In a tally chart, the group of tally marks ∣∣∣∣ ∣\cancel{||||}\,| represents the number:

  • A) 4
  • B) 5
  • C) 6
  • D) 11

Q3. A pie chart represents a total of 100%. What angle at the centre represents 25% of the data?

  • A) 25∘25^\circ
  • B) 45∘45^\circ
  • C) 90∘90^\circ
  • D) 180∘180^\circ

Q4. Which diagram is BEST for showing how one quantity changes over time?

  • A) Pie chart
  • B) Line graph
  • C) Bar chart
  • D) Pictogram

Q5. For the data set 3,7,7,9,143, 7, 7, 9, 14, the mode is:

  • A) 7
  • B) 8
  • C) 9
  • D) 14

Q6. The range of the data set 12,5,18,9,512, 5, 18, 9, 5 is:

  • A) 5
  • B) 9
  • C) 13
  • D) 18

Q7. A fair six-sided die is rolled. What is P(rolling a 3)P(\text{rolling a } 3)?

  • A) 12\dfrac{1}{2}
  • B) 13\dfrac{1}{3}
  • C) 16\dfrac{1}{6}
  • D) 36\dfrac{3}{6}

Q8. If P(A)=0.7P(A) = 0.7, then P(A′)P(A') (the complement) equals:

  • A) 0.70.7
  • B) 0.30.3
  • C) 1.71.7
  • D) 00

Q9. In a pictogram, one symbol 🍎 represents 4 apples. How many apples do 🍎🍎🍎 represent?

  • A) 3
  • B) 7
  • C) 12
  • D) 4

Q10. The median of 2,4,6,8,102, 4, 6, 8, 10 is:

  • A) 4
  • B) 5
  • C) 6
  • D) 30

Section B — Matching (1 mark each, 5 marks)

Q11–Q15. Match each term in the left column to its correct description on the right. Write the letter.

Term Description
Q11. Mean A) Most frequently occurring value
Q12. Mode B) The middle value when data is ordered
Q13. Median C) Sum of values divided by number of values
Q14. Range D) A list of all possible outcomes
Q15. Sample space E) Highest value minus lowest value

Section C — True / False WITH Justification (2 marks each, 10 marks)

State True or False (1 mark) and give a one-line justification (1 mark).

Q16. "The probability of any event is always a number between 0 and 1 inclusive."

Q17. "A scatter plot showing points rising from bottom-left to top-right indicates a negative correlation."

Q18. "For the data 5,5,5,55, 5, 5, 5, the range is 0."

Q19. "Information taken from a published government census report is an example of primary data."

Q20. "If a bag contains only red and blue balls, and P(red)=25P(\text{red}) = \dfrac{2}{5}, then P(blue)=35P(\text{blue}) = \dfrac{3}{5}."

Answer keyMark scheme & solutions

Section A (1 mark each)

Q1. B — Primary data is collected first-hand by the researcher; secondary is from existing sources. (1)

Q2. C — ∣∣∣∣\cancel{||||} is a bundle of 5, plus 1 extra =6= 6. (1)

Q3. C — 25%25\% of 360∘=0.25×360=90∘360^\circ = 0.25 \times 360 = 90^\circ. (1)

Q4. B — Line graphs display continuous change over time. (1)

Q5. A — 7 appears twice, more than any other value → mode =7= 7. (1)

Q6. C — Range == max −- min =18−5=13= 18 - 5 = 13. (1)

Q7. C — One favourable outcome out of six: P=16P = \dfrac{1}{6}. (1)

Q8. B — P(A′)=1−P(A)=1−0.7=0.3P(A') = 1 - P(A) = 1 - 0.7 = 0.3. (1)

Q9. C — 3×4=123 \times 4 = 12 apples. (1)

Q10. C — Ordered data, middle (3rd of 5) value is 6. (1)

Section B (1 mark each)

Q11. C (Mean = sum ÷ count) Q12. A (Mode = most frequent) Q13. B (Median = middle value) Q14. E (Range = highest − lowest) Q15. D (Sample space = list of all outcomes) (5 marks total)

Section C (2 marks each: 1 for T/F, 1 for reason)

Q16. True (1) — Probabilities range from 0 (impossible) to 1 (certain); none can exceed this. (1)

Q17. False (1) — Points rising left→right show positive correlation, not negative. (1)

Q18. True (1) — Max − min =5−5=0= 5 - 5 = 0; all values equal so range is 0. (1)

Q19. False (1) — A census report is an existing published source, so it is secondary data. (1)

Q20. True (1) — Only two outcomes, so P(blue)=1−25=35P(\text{blue}) = 1 - \dfrac{2}{5} = \dfrac{3}{5}. (1)

[
  {"claim":"25% of 360 degrees = 90", "code":"result = (Rational(25,100)*360 == 90)"},
  {"claim":"Range of 12,5,18,9,5 is 13", "code":"data=[12,5,18,9,5]; result = (max(data)-min(data) == 13)"},
  {"claim":"Complement of P(A)=0.7 is 0.3", "code":"result = (1 - Rational(7,10) == Rational(3,10))"},
  {"claim":"Median of 2,4,6,8,10 is 6", "code":"d=sorted([2,4,6,8,10]); result = (d[len(d)//2] == 6)"},
  {"claim":"P(blue)=3/5 when P(red)=2/5", "code":"result = (1 - Rational(2,5) == Rational(3,5))"}
]