Statistics Worksheet — GCSE — Intermediate

Statistics worksheet for Key Stage 4 / GCSE (Ages 14-16). Intermediate level maths practice, aligned to the UK National Curriculum. Print-ready with answer key included.

Maths•Key Stage 4 / GCSE (Ages 14-16)•Statisticsintermediate

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Exploring Statistics: Intermediate Level Challenges

Key Stage 4 / GCSE (Ages 14-16) - Intermediate

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Instructions: This worksheet is designed to deepen your understanding of statistical concepts through a variety of problem-solving and data analysis tasks. Work through each activity carefully, showing all calculations and reasoning where required.

Data Interpretation

Study the data provided in the table below and answer the questions. Use your knowledge of statistics to interpret the data accurately.

Month	Temperature (°C)	Rainfall (mm)	Sunny Days
January	5	78	10
February	6	54	12
March	9	62	15
April	12	45	18
May	16	30	22

1. Which month had the highest average temperature?

2. Calculate the total rainfall for the first quarter of the year.

3. What is the average number of sunny days per month?

Probability Scenarios

Read each scenario and calculate the probability of the given event. Express your answer as a fraction, decimal, or percentage.

1. A bag contains 4 red, 5 blue, and 6 green marbles. What is the probability of drawing a blue marble?

2. A die is rolled. What is the probability of rolling an even number?

3. A card is drawn from a standard deck of 52 cards. What is the probability of drawing a Queen?

Measures of Central Tendency

Calculate the mean, median, and mode for the given data set. Show all your workings clearly.

Data Set: 12, 15, 12, 18, 16, 15, 19, 12

1. Mean:

2. Median:

3. Mode:

Box Plot Analysis

Examine the box plot below and answer the questions. Use your understanding of quartiles and interquartile range.

Box Plot Data: Min = 5, Q1 = 10, Median = 15, Q3 = 20, Max = 25

1. What is the interquartile range (IQR)?

2. Identify any potential outliers.

Scatter Plot Interpretation

Consider the scatter plot showing the relationship between study hours and exam scores. Answer the questions based on the trend observed.

1. Describe the correlation between study hours and exam scores.

2. Predict the exam score for a student who studies for 8 hours.

Standard Deviation Calculation

Calculate the standard deviation for the following data set. Use the formula for standard deviation and show all steps.

Data Set: 4, 8, 6, 5, 3, 7

Standard Deviation:

Venn Diagram Problem

Use the Venn diagram to solve the problem. The diagram shows the number of students who like maths, science, and both subjects.

Maths: 30, Science: 25, Both: 10

1. How many students like only maths?

2. How many students like only science?

3. How many students like either maths or science or both?

Extended Writing: Statistical Report

Write a detailed report analysing the effectiveness of a new teaching method based on the following data. Discuss the implications and provide recommendations.

Data: Before Method - Mean Score = 65, After Method - Mean Score = 75

Evaluate the impact of the teaching method on student performance. Consider factors such as mean score improvement, potential biases, and any external influences. [15 marks]

Answer Key

Activity 1: May ; 194 mm ; 15.4

Activity 2: 5/15 or 1/3 ; 1/2 or 50% ; 4/52 or 1/13

Activity 3: 14.875 ; 15 ; 12

Activity 4: 10 ; None

Activity 5: Positive correlation ; Approximately 80

Activity 6: 1.87

Activity 7: 20 ; 15 ; 45

Activity 8: Evaluative answers will vary