Year 9 Statistics and Probability Worksheet - Intermediate

Year 9 Statistics and Probability worksheet for Year 9 (Key Stage 3 / Year 7-9 (Ages 11-14)). Intermediate level maths practice, aligned to the UK National Curriculum. Print-ready with answer key included.

Maths•Key Stage 3 / Year 7-9 (Ages 11-14)•Statistics and Probabilityintermediate

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Year 9 Statistics and Probability: Data, Distributions and Chance

Key Stage 3 • Ages 13–14 • Intermediate

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Instructions: Show your working clearly and include units where appropriate. For estimated means, use class midpoints; for probability, give fractions in their simplest form unless a decimal is requested.

Estimating the Mean from Grouped Data

Use the midpoint of each class interval as the representative value. Multiply each midpoint by its frequency, add the products, then divide by the total frequency. Give your estimated mean to 1 decimal place where needed.

The table shows the time, in minutes, taken by 30 pupils to travel to school.

Travel time (minutes)	Frequency
0–10	4
10–20	9
20–30	11
30–40	6

1. Write down the midpoint of each class interval. [2 marks]

2. Calculate the estimated mean travel time. [3 marks]

Compare Two Distributions

Use the data in the table to calculate each group’s mean and range. Then compare the groups using both statistics, referring to the context. Show calculations where needed.

Scores out of 20 in two quizzes:

Quiz	Group A	Group B
Pupil 1	8	11
Pupil 2	12	13
Pupil 3	14	14
Pupil 4	16	15
Pupil 5	20	17

1. Calculate the mean score for Group A and Group B. [3 marks]

2. Calculate the range for each group. [2 marks]

3. Compare the groups using their means and ranges. [3 marks]

Tree Diagrams: Two-Step Events

A tree diagram lists each possible outcome at each stage. Multiply probabilities along a path to find the probability of that combined outcome. For a fair coin, the probability of heads and tails is 1/2 each.

A fair coin is tossed twice. Use the outcomes H and T.

1. Complete the probability tree by writing H (1/2) and T (1/2) on each set of branches, then list the four possible outcomes. [2 marks]

2. Find the probability of getting two heads. [1 mark]

3. Find the probability of getting exactly one head. [2 marks]

Combined Events with a Bag

A counter is selected, replaced, and then a second counter is selected, so the probabilities stay the same on both stages. Use multiplication for a path through the tree and add relevant path probabilities when an event can happen in more than one way.

A bag contains 3 red counters and 2 blue counters. One counter is drawn, replaced, and then another is drawn.

1. Write the probability of red and blue at each stage of a tree diagram. [2 marks]

2. Find the probability of drawing two red counters. [2 marks]

3. Find the probability of drawing one red and one blue, in either order. [3 marks]

Experimental and Theoretical Probability

Theoretical probability is calculated from equally likely outcomes. Experimental probability is the observed frequency divided by the number of trials. Compare the two and comment on how results may change as the number of trials increases.

A fair six-sided die is rolled 120 times. The results are shown below.

Score	1	2	3	4	5	6
Frequency	18	22	17	23	19	21

1. What is the theoretical probability of rolling a 4? [1 mark]

2. Calculate the experimental probability of rolling a 4. [2 marks]

3. Compare the experimental and theoretical probabilities of rolling a 4. [2 marks]

4. Explain what may happen to the experimental probability if the die is rolled many more times. [2 marks]

Answer Key

Activity 1: 5, 15, 25, 35 ; (5×4 + 15×9 + 25×11 + 35×6) ÷ 30 = 590 ÷ 30 ≈ 19.7 minutes

Activity 2: Group A mean = 14, Group B mean = 14 ; Group A range = 12, Group B range = 6 ; Both groups have the same mean, but Group B’s scores are less spread out because its range is smaller

Activity 3: Branches at each toss: H = 1/2, T = 1/2 ; Outcomes: HH, HT, TH, TT ; P(two heads) = 1/4 ; P(exactly one head) = 1/2

Activity 4: At each stage, P(red) = 3/5 and P(blue) = 2/5 ; P(two red) = 3/5 × 3/5 = 9/25 ; P(one red and one blue) = (3/5 × 2/5) + (2/5 × 3/5) = 12/25

Activity 5: Theoretical probability = 1/6 ; Experimental probability = 23/120 ; 1/6 = 20/120, so the experimental probability is 3/120 (1/40) higher ; With many more rolls, the experimental probability is likely to get closer to 1/6