Year 8 Statistics and Probability Worksheet - Intermediate

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

Ages 12–13 | Key Stage 3 | Intermediate

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Instructions: Work through the activities in order, showing your working in the answer spaces. Use the data provided to support your conclusions, and label axes clearly when drawing a graph. Check that probabilities for a complete set of outcomes add up to 1.

Investigate the Correlation

The table shows how long six students revised and their quiz scores. Plot each pair on a scatter graph, with revision time on the horizontal axis and quiz score on the vertical axis. Use a suitable scale and label both axes. Then answer the questions using the plotted points.

Revision time (hours)	Quiz score (%)
0	42
1	50
2	56
3	63
4	69
5	74

1. Draw the scatter graph on the grid provided by your teacher. [3 marks]

2. Describe the correlation between revision time and quiz score. [2 marks]

3. Use the trend in the data to estimate the quiz score for a student who revised for 3.5 hours. [2 marks]

Read a Scatter Graph in Context

Use the stated features of each scatter graph to identify the relationship. Correlation describes an association; it does not by itself prove that one variable causes the other. Give a brief reason for each conclusion.

1. As the outdoor temperature rises, ice-cream sales tend to rise. What type of correlation would you expect between temperature and sales? [2 marks]

2. A scatter graph of distance travelled and petrol remaining shows points trending downwards from left to right. Describe the correlation. [2 marks]

3. A scatter graph of shoe size and reading test score has points scattered with no clear pattern. Describe the correlation. [2 marks]

4. A strong positive correlation is found between hours of practice and performance score. Does this prove that practice is the only cause of higher scores? Explain briefly. [2 marks]

Averages from a Frequency Table

The table gives the number of books read by a group of students during one month. For the mean, multiply each number of books by its frequency, add these products, and divide by the total frequency. For the median, use the ordered positions represented by the frequencies.

Books read	Frequency
0	2
1	5
2	4
3	1

1. How many students are represented in the table? [1 mark]

2. Find the mode number of books read. [1 mark]

3. Find the mean number of books read. [2 marks]

4. Find the median number of books read. [2 marks]

Build a Two-Event Sample Space

A fair coin is tossed and a fair six-sided die is rolled. List ordered pairs as (coin result, die result), so that each outcome is shown once. Use the sample space to answer the questions.

Coin result	1	2	3	4	5	6
Heads
Tails

2. How many equally likely outcomes are in the complete sample space? [1 mark]

3. How many outcomes show a tail and an even number? [1 mark]

Probabilities Add to One

For each complete set of outcomes, the probabilities must total 1. Find missing probabilities by subtracting the known probabilities from 1. State any probability as a fraction in its simplest form.

1. A spinner has outcomes red, blue and yellow. P(red) = 1/4 and P(blue) = 1/2. Find P(yellow). [2 marks]

2. A bag contains only green and purple counters. P(green) = 0.37. Find P(purple). [2 marks]

3. A fair six-sided die is rolled. Find the probability of not rolling a 5. [2 marks]

4. A random day is chosen from a seven-day week. P(weekday) = 5/7. Find P(weekend), then show that the two probabilities sum to 1. [2 marks]

Answer Key

Activity 1: Plot (0,42), (1,50), (2,56), (3,63), (4,69), (5,74), with revision time (hours) on the horizontal axis and quiz score (%) on the vertical axis ; positive correlation ; approximately 66% (a reasonable estimate from the trend)

Activity 2: Positive correlation ; negative correlation ; no correlation ; No. Correlation does not prove causation, and other factors may contribute.

Activity 3: 12 students ; 1 book ; 1.5 books ; 1 book

Activity 4: Heads row: (Heads,1), (Heads,2), (Heads,3), (Heads,4), (Heads,5), (Heads,6) ; Tails row: (Tails,1), (Tails,2), (Tails,3), (Tails,4), (Tails,5), (Tails,6) ; 12 outcomes ; 3 outcomes

Activity 5: 1/4 ; 0.63 ; 5/6 ; 2/7, and 5/7 + 2/7 = 1