KS3Solutions

Statistics

Answers grouped by subtopic.

Back to questions

Averages

  1. S-Q1
    Answer
    A frequency table has values 2, 4, 6 with frequencies 1, 2, 1. Find the mean.
    Working
    1. Total score = (2 × 1) + (4 × 2) + (6 × 1) = 2 + 8 + 6 = 16.
    2. Total frequency = 1 + 2 + 1 = 4.
    3. Mean = 164 = 4.
    Answer: 4
  2. S-Q2
    Answer
    Find the median of 3, 5, 7, 9, 11.
    Working
    1. The middle value is 7, so the median is 7.
    Answer: 7
  3. S-Q3
    Answer
    Find the mode of 2, 3, 3, 4, 5.
    Working
    1. 3 appears most often, so the mode is 3.
    Answer: 3
  4. S-Q5
    Answer
    The times in minutes are 10, 12, 14, 16. Find the mean.
    Working
    1. Sum = 10 + 12 + 14 + 16 = 52.
    2. Mean = 524 = 13.
    Answer: 13

Range

  1. S-Q4
    Answer
    Find the range of 2, 6, 9, and 12.
    Working
    1. Range = largest - smallest = 12 - 2 = 10.
    Answer: 10

Tables and graphs

  1. S-Q6
    Answer
    A frequency table has values 5, 10, 15 with frequencies 1, 2, 1. Find the mean.
    Working
    1. Total score = (5 × 1) + (10 × 2) + (15 × 1) = 5 + 20 + 15 = 40.
    2. Total frequency = 1 + 2 + 1 = 4.
    3. Mean = 404 = 10.
    Answer: 10

Scatter graphs

  1. S-Q7
    Answer
    A scatter graph shows points rising from left to right. Describe the correlation.
    Working
    1. As 𝑥 increases, 𝑦 tends to increase, so the correlation is positive.
    Answer: Positive correlation
  2. S-Q8
    Answer
    A line of best fit passes through (0, 2) and (10, 12). Estimate 𝑦 when 𝑥 = 5.
    Working
    1. Slope = (12 - 2)(10 - 0) = 1010 = 1.
    2. Equation is 𝑦 = 𝑥 + 2.
    3. When 𝑥 = 5, 𝑦 = 7.
    Answer: 7
Basira Institute · Basira Group