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# Frequency trees for Edexcel GCSE Maths

1. Recording data using trees
2. Describing data presented in trees
3. Analysing the frequency of outcomes from trees

A frequency tree can be used to record frequencies of outcomes and to calculate probabilities. The different branches of frequency trees state the frequency of outcomes.

Frequency trees can be used to interpret and describe trends using the results of an experiment.

The frequencies given on a frequency tree can be used to calculate the probability of outcomes.

# 1

Given the frequency tree, calculate the missing values x, y and z.

2x + x + 70 = 100
3x = 30
x = 10

y + 5 = 20
y = 15

z + 3 = 10
z = 7

x = 10, y = 15, z = 7

# 2

A frequency tree is given for 50 students. Calculate the probability that a student is sporty.

number of students that are sporty = 13 + 11 = 24
probability that a student is sporty = 24 รท 50 = 0.48

0.48

# 3

A group of twenty random students are asked if they walked or took the bus to school on a specific day and if they were late or not. The findings of the survey are given in the frequency tree. Interpret the results.

Most students (12) took the bus on that day, and 8 walked to school. Out of the students that walked, only 2 were late and 6 were not. Out of the students that took the bus, 7 were late and 5 were not. This shows that a student that takes the bus is more likely to be late to school than a student that walks to school. Also, a student is more likely to take the bus to school than walk.

# 4

A group of 15 Drama and 20 Literature students are asked whether they prefer movies or books. Calculate the probability that a student prefers movies.

Number of students that prefer movies = 10 + 5 = 15.
Total number of students = 15 + 20 = 35.
Probability that a student prefers movies = 15/35 = 3/7.

# 5

Twenty students are asked whether they have siblings or not and if they ever get bored at home. A frequency tree is given to represent this data. Calculate the probability that a student with siblings gets bored at home.

P(student with siblings gets bored) = 2/14 = 1/7

1/7

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