Year 9 Statistics and Probability Worksheet - Beginner

Year 9 Statistics and Probability worksheet for Year 9 (Key Stage 3 / Year 7-9 (Ages 11-14)). Beginner 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 Probabilitybeginner

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Year 9 Statistics and Probability: Data, Trees and Chance

Ages 13–14 | Beginner | Key Stage 3

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Instructions: Work through the activities in order, showing your calculations in the answer spaces. For grouped data, use each class midpoint as a representative value; for comparisons, support your conclusion with the average and range. Tree branches show successive outcomes, and the probabilities along a complete route are multiplied.

Estimate the Mean from Grouped Data

Find the midpoint of each class interval, then multiply each midpoint by its frequency. Add the products and divide by the total frequency. The first midpoint is shown as a reminder: the midpoint of 10–19 is 14.5.

Time (minutes)	Frequency	Midpoint
10–19	4	14.5
20–29	6
30–39	8

1. Complete the two missing class midpoints. [2 marks]

2. Calculate the estimated mean time. Show your working. [3 marks]

Compare Two Distributions

Use the data table to find the mean and range for each group. Compare both measures, then make a clear statement about which group has the higher average and which is more consistent. The range is the largest value minus the smallest value.

Group	Test score 1	Test score 2	Test score 3	Test score 4	Test score 5
A	12	14	15	17	22
B	10	15	16	18	21

1. Calculate the mean score for Group A and Group B. [2 marks]

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

3. Which group has the higher mean, and which has the greater spread? Use your results to explain briefly. [2 marks]

Build a Tree Diagram: Two Coin Tosses

For each toss, the possible outcomes are Heads (H) and Tails (T), each with probability 1/2. Complete the route probabilities by multiplying along each route. Then use the four equally likely outcomes to answer the questions.

First toss: H (1/2) or T (1/2).

From each first-toss outcome, the second toss is H (1/2) or T (1/2).

1. Complete the probabilities for the routes HH and HT. [2 marks]

2. Complete the probabilities for the routes TH and TT. [2 marks]

3. What is the probability of getting exactly one Head? [1 mark]

Tree Diagram: Choosing a Snack

A pupil chooses one fruit and then one drink. Each fruit is equally likely, and each drink is equally likely. Use the listed branches to work out the probability of each complete outcome by multiplying the branch probabilities.

Fruit branches: apple (1/2), banana (1/2).

From either fruit: water (1/3), milk (1/3), juice (1/3).

1. What is the probability of apple and juice? [1 mark]

2. What is the probability of banana and milk? [1 mark]

3. What is the probability of choosing a banana and any drink? [1 mark]

Experimental and Theoretical Probability

A fair six-sided die has theoretical probability 1/6 of landing on a 6. Use the table to calculate the experimental relative frequency of a 6 for each number of rolls. Compare the experimental results with the theoretical probability.

Trial	Number of rolls	Number of sixes
1	60	8
2	120	17
3	300	48

1. Calculate the experimental probability of a 6 in Trial 1. [1 mark]

2. Calculate the experimental probability of a 6 in Trial 2. [1 mark]

3. Which trial's experimental probability is closer to the theoretical probability of 1/6? Show or explain your comparison. [2 marks]

Chance in Context

A bag contains 3 red counters and 2 blue counters. One counter is selected at random, its colour is recorded, and it is replaced before the next selection. Use the probabilities for each selection to reason about the combined outcomes.

For each selection: P(red) = 3/5 and P(blue) = 2/5. The counter is replaced before the second selection.

1. Find the theoretical probability of red followed by blue. [2 marks]

2. Find the theoretical probability of two red counters in a row. [2 marks]

3. In 100 repeated two-selection trials, 25 results are red followed by blue. Find the experimental probability of red followed by blue. [1 mark]

Answer Key

Activity 1: Midpoints: 24.5 ; 34.5. Estimated mean: (14.5×4 + 24.5×6 + 34.5×8) ÷ 18 = 459 ÷ 18 = 25.5 minutes.

Activity 2: Group A mean = 16; Group B mean = 16. Group A range = 10; Group B range = 11. The means are equal; Group B has the greater spread and Group A is more consistent.

Activity 3: HH = 1/4 ; HT = 1/4 ; TH = 1/4 ; TT = 1/4. Exactly one Head = 1/2.

Activity 4: Apple and juice = 1/6. Banana and milk = 1/6. Banana and any drink = 1/2.

Activity 5: Trial 1 = 8/60 = 2/15. Trial 2 = 17/120. Trial 2 is closer to 1/6: |17/120 − 1/6| = 1/120, while |2/15 − 1/6| = 1/30.

Activity 6: Red then blue = (3/5)×(2/5) = 6/25. Two reds = (3/5)×(3/5) = 9/25. Experimental probability = 25/100 = 1/4.