Year 8 Statistics and Probability Worksheet - Beginner

Year 8 Statistics and Probability worksheet for Year 8 (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 8 Statistics and Probability: Data Detectives

Ages 12–13 • Beginner • UK National Curriculum

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Instructions: Work through each activity, showing your calculations where needed. Use the provided data to draw and interpret graphs, calculate averages, and list outcomes. Remember that probabilities for all possible outcomes add up to 1.

Plot the Data: Revision Time and Quiz Scores

Use the table to plot each pair of values on graph paper: revision time (hours) on the horizontal axis and quiz score on the vertical axis. Choose a suitable scale and label both axes. Draw a line of best fit, then describe the relationship you see.

Revision time (hours)	Quiz score (%)
1	42
2	50
3	58
4	65
5	74

1. Describe the correlation between revision time and quiz score.

2. Give one reason why the points may not all lie exactly on your line of best fit.

3. Use your line of best fit to estimate the quiz score for 3.5 hours of revision.

Read and Interpret a Scatter Graph

Read the paired values in the table as points on a scatter graph. Decide whether the relationship is positive, negative or shows no clear correlation. Use the data to support your answers.

Outdoor temperature (°C)	Hot drinks sold
8	52
12	43
16	35
20	26

1. Describe the correlation between temperature and hot drinks sold.

2. What happens to hot drinks sales as the temperature rises?

3. Would you use this pattern to predict sales at 30°C? Give one reason for your answer.

Find Averages from a Frequency Table

The table shows the number of books read by pupils during a half-term. For the mean, multiply each number of books by its frequency, add those products, then divide by the total frequency. For the median, use the positions of the ordered data values.

Number of books	Frequency
0	2
1	4
2	5
3	3

1. How many pupils are represented in the table?

2. Find the mode number of books.

3. Find the mean number of books.

4. Find the median number of books.

Build a Sample Space: Two Coins

A fair coin is flipped twice. Use the sample space table to list every ordered outcome, where the first letter is the first flip and the second letter is the second flip. Then answer the questions below.

First flip / second flip	Heads	Tails
Heads	HH	HT
Tails	TH	TT

1. Write the complete set of possible outcomes.

2. How many outcomes contain exactly one head?

3. What is the probability of getting two tails?

Sample Space: Choose a Snack and a Drink

A pupil chooses one snack and one drink. The table lists all possible combinations. Each combination is equally likely. Use the table to count outcomes and calculate probabilities.

Snack	Water
Juice	Milk
Apple	Apple-water
Apple-juice	Apple-milk
Biscuit	Biscuit-water
Biscuit-juice	Biscuit-milk
Carrot sticks	Carrot-water
Carrot-juice	Carrot-milk

1. How many possible snack-and-drink outcomes are there?

2. List the outcomes that include juice.

3. What is the probability of choosing carrot sticks and milk?

Probabilities Add to One

For each situation, the listed outcomes cover every possible result. Add the probabilities to check they total 1. Use the fact that the probability of an event and its complement sum to 1.

1. A spinner has outcomes red, blue and green. P(red) = 0.2 and P(blue) = 0.5. Find P(green).

2. A weather forecast gives P(rain) = 0.35. Find P(no rain).

3. A bag contains only red and yellow counters. P(red) = 3/8. Find P(yellow).

4. A game has outcomes win, draw and lose, with probabilities 0.4, 0.25 and 0.35. Show that the probabilities of all outcomes sum to 1.

Answer Key

Activity 1: Plot the points (1,42), (2,50), (3,58), (4,65), (5,74); upward trend; positive correlation; individual differences or other factors can affect scores; estimate from the drawn line, approximately 62–63%.

Activity 2: Negative correlation; sales decrease as temperature rises; no, 30°C is outside the data range, so this would be an extrapolation and may not follow the same pattern.

Activity 3: 14 pupils ; 2 books ; 25/14 ≈ 1.79 books ; 2 books.

Activity 4: HH, HT, TH, TT ; 2 ; 1/4.

Activity 5: 9 ; Apple-juice, Biscuit-juice, Carrot-juice ; 1/9.

Activity 6: 0.3 ; 0.65 ; 5/8 ; 0.4 + 0.25 + 0.35 = 1.