# data[].attributes.attachment_link.title
Bar Charts, Pie Charts, Histograms, Stemplots, Timeplots (1.2)

# data[].attributes.body
CENSUS INFORMATION CARDS: https://docs.google.com/document/d/1pfm8qT83mHSec5I4JjzZAiyRiTgiWPyxmp3Mu-c2jOo/edit?usp=sharing

# data[].attributes.headline
Print out your final work in A4 size (less than 6 pages) or A3 size (less than 3 pages)

# data[].attributes.subject
Print out your final work in A4 size (less than 6 pages) or A3 size (less than 3 pages)

# data[].attributes.body
Correct answers (on last two pages of document).

# data[].attributes.attachment_link.title
Mean, Median, Mode, and Range - How To Find It!

# data[].attributes.headline
VIDEO TUTORIAL: Scatterplot and line of best fit

# data[].attributes.subject
VIDEO TUTORIAL: Scatterplot and line of best fit

# data[].attributes.attachment_link.title
Creating a scatterplot and drawing a line of best fit

# data[].attributes.headline
Stem and Leaf Plots - one and two sided 

# data[].attributes.subject
Stem and Leaf Plots - one and two sided 

# data[].attributes.attachment_link.title
STATISTICS: Grouped Frequency Table and Histograms

# data[].attributes.headline
ACTIVITY PPT - HOW WELL TRAVELLED IS OUR CLASS?

# data[].attributes.subject
ACTIVITY PPT - HOW WELL TRAVELLED IS OUR CLASS?

# data[].attributes.headline
SUBMISSION FORM & GROUPINGS FOR DATA ASSIGNMENT (Tab 1 - 8A, Tab 2 - 8B)

# data[].attributes.subject
SUBMISSION FORM & GROUPINGS FOR DATA ASSIGNMENT (Tab 1 - 8A, Tab 2 - 8B)

# data[].attributes.body
1. WK 1: Enter your project question next to your group and the grade you are aiming for.
2. WK 1: Tick off when you are done with your introduction.
3. WK 2: Enter a link to your survey IF NEEDED so your teacher can send it to other classes/teachers if needed.
4. WK 2: Tick off when you are done with your frequency table and data collection.
5. WK 3: Tick off when you are done with your graph.
6. WK 4: Tick of when you have found your averages.
7. WK 4: Tick of when you have written your conclusion.
8. Submit a link to your assignment (make sure anyone can view it).

# data[].attributes.body
If you know how to create a linear equation you can answer the questions referring to equation (these is bonus however and optional).

# data[].attributes.headline
WORKSHEET: HOW WELL TRAVELLED IS YOUR CLASS?

# data[].attributes.subject
WORKSHEET: HOW WELL TRAVELLED IS YOUR CLASS?

# data[].attributes.headline
WORKSHEET: Finding Mean Median and Mode practice [merits challenge]

# data[].attributes.subject
WORKSHEET: Finding Mean Median and Mode practice [merits challenge]

# data[].attributes.attachment_link.title
TYPES OF DATA and GRAPHS student worksheet

# data[].attributes.body
Also state the type of data and find the mean, median, mode and range

# data[].attributes.body
BD-DA: All averages
DS - Finding mean, median, mode from frequency tables

# data[].attributes.attachment_link.readable_text
Providing coverage for a range of international curricula for ages 5-18, MyiMaths offers interactive lessons, "booster packs" for revision, and assignable homeworks and worksheets, along with a wealth of resources that will help you deliver your teaching in the classroom and at home to develop your students' confidence and fluency in maths

# data[].attributes.attachment_link.description
MyiMaths is an interactive online teaching and homework subscription website for schools that provides coverage for a range of international curricula for ages 11-18 including the International Baccalaureate, Cambridge Assessment International Education, Edexcel and OxfordAQA. MyiMaths offers a wealth of resources that will help you deliver your teaching in the classroom and develop your students' confidence and fluency in maths.

# data[].attributes.attachment_link.description
Easily create surveys and polls to collect customer feedback, measure employee satisfaction, and organize team events.

# data[].attributes.attachment_link.title
Two Sided Stem and Leaf Plots: Examples (Basic Probability and Statistics Concepts)

# data[].attributes.attachment_link.title
Find Range Mode Median Mean with a Frequency Table

# data[].attributes.body
Are you able to.....

1. Create a scatter plot (SALTy)

2. Create the best fit line

3. Describe the trend (positive/ negative, strong/ weak/ no correlation)

4. Use the best fit line to predict X or Y

5. Draw back-to-back stem plot of data

6. Find out the mean, median, mode and range

7. Compare and contrast the two data sets in stem and leaf plots.

# data[].attributes.attachment_link.description
Averages from frequency tables GCSE maths revision guide, step by step examples, exam questions and averages from frequency tables worksheet.

# data[].attributes.attachment_link.readable_text
One to one maths interventions built for KS4 success

Weekly online one to one GCSE maths revision lessons now available

Learn more

Here we will learn about the median from a frequency table, including what the median is and how to find it. We will also look at finding the class which contains the median from grouped frequency tables.

There are also averages from frequency tables worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you're still stuck.

Median from a frequency table is when we find the median average from a data set which has been organised into a frequency table.

The median is the middle value and is a measure of central tendency, it is a value that can be used to represent a set of data.

We can calculate the median by:

a) Writing down each of the values in the table and crossing off values to find the middle value.

E.g.
The frequency table shows the number of cars owned by 13 families:

We can use the table to write down each of the values

The middle number is 1 , so the median number of cars is 1 .

b) Using the median formula and cumulative frequency

If the data set is large we can us the formula to work out the position of the median \text{Position of the median}=(\frac{n+1}{2})^\text{th} , and cumulative frequency to find the actual median value.

Cumulative frequency is where we add up the numbers in the frequency column as we go down the table.

E.g.

The total number of values is 13 , so n=13 .

So the, \text{Position of the median}=(\frac{n+1}{2})^\text{th}=(\frac{13+1}{2})^\text{th}=7^\text{th}

The 7^\text{th} value is in the row of the table that contains the 5^\text{th} , 6^\text{th} , 7^\text{th} , 8^\text{th} , and 9^\text{th} values.

So the median number of cars = 1 .

What is median from a frequency table?

In order to find the median from a frequency table:

1. Find the position of the median.

2. Work out the cumulative frequencies.

3. Work out the median.

4. Write down the median.

How to find the median from a frequency table

Averages including median from a frequency table worksheet

Get your free averages from a frequency table worksheet of 20+questions and answers. Includes reasoning and applied questions on median from a frequency table.

DOWNLOAD FREE

x

Averages including median from a frequency table worksheet

Get your free averages from a frequency table worksheet of 20+questions and answers. Includes reasoning and applied questions on median from a frequency table.

DOWNLOAD FREE

Related lessons on frequency tables

Median from a frequency table is part of our series of lessons to support revision on frequency tables. You may find it helpful to start with the main frequency table lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:

Example 1: frequency table - odd number of values

The frequency table shows the ages in years of 15 people in a sports club.

Find the median of age from this set of data.

Find the position of the median.

There are 15 values, so n=15 .

\text{Position of the median}=(\frac{n+1}{2})^\text{th}=(\frac{15+1}{2})^\text{th}=8^\text{th}

2 Work out the cumulative frequencies.

Go down the frequencies, adding them up as you go along.

3 Work out the median.

We use the cumulative frequencies to find where the 8^\text{th} value is. This row contains the 8^\text{th} to 14^\text{th} values.

4 Write down the median.

The final step is to write down the median value

The median is 14 years

Common misconceptions

Check which average you are being asked for

Check if you have been asked for the median, mode or mean average.

The value given by the median formula is not for the median, but for the position of the median. The formula gives us where the middle value is.

When there is an odd number of data there is a single middle value for the median.
When there is an even number of data, there is a middle pair of values and you then need to find the midpoint of these values.

E.g.
The middle pair of values is 9 and 13 . The mid-point of these is 11 . The median is 11 .

\frac{9+13}{2}=\frac{22}{2}=11

The class intervals used in grouped frequency tables can be written in different ways. Take care when writing them, or finding the midpoints.

E.g.

0 to 5

0-5

0\le x<5

Frequency distribution table

A frequency distribution table is the same as a frequency table

1. The table shows the number of people living in 17 flats.

Find the median number of people living in a flat.
(1 mark)

2
For the correct answer
(1)

2. The table shows the heights of 15 children.

Find the class interval that contains the median.
(1 mark)

130\le x <140
For the correct answer
(1)

3. The table shows the scores when a dice is rolled.

(a) Explain why the median cannot be 7 .

(b) Find the median score.
(2 marks)

(a)

The median cannot be 7 as it it not one of the scores
(1)
(b)

4
(1)

Learning checklist

You have now learned how to:

Find the median from a frequency table

Find the class interval which contains the median from a grouped frequency table

Still stuck?

Prepare your KS4 students for maths GCSEs success with Third Space Learning. Weekly online one to one GCSE maths revision lessons delivered by expert maths tutors.

Find out more about our GCSE maths tuition programme.

We use essential and non-essential cookies to improve the experience on our website. Please read our Cookies Policy for information on how we use cookies and how to manage or change your cookie settings. Accept

# data[].attributes.attachment_link.description
Median from a frequency table GCSE maths revision guide, step by step examples, exam questions and median from a frequency table worksheet.

# data[].attributes.attachment_link.readable_text
One to one maths interventions built for KS4 success

Weekly online one to one GCSE maths revision lessons now available

Learn more

Here we will learn about two way tables, including what a two way table is, how to construct them, interpret them, and how to calculate the probability of an event using a two way table.

There are also two way tablesworksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you're still stuck.

What are two way tables?

Two way tables are a type of frequency table used for organising data. They are also known as contingency tables.

Two way tables are mostly used for categorical data, though they can be used for numerical data too. Categorical data is data where the items are words rather than numbers.

For example, colours, sports, and car manufacturers.

To construct a two way table, we need two categorical variables. One variable is featured as the top row within the two way table, and the other variable features on the first column of the table.

For example,

This two way table shows a data set about what students eat for lunch. One categorical variable is the gender of the child, the other categorical variable is what type of lunch they have.

There are row and column totals. So we can see that there are 35 boys and that 50 students have packed lunch. The total number of students in the table is 90.

How to construct two way tables

In order to construct two way tables:

1. Fill in the known values into the two way table.

2. Calculate missing values.

3. Calculate the row and column totals.

4. Check the final total.

Explain how to construct two way tables

Two way tables worksheet

Get your free two way tables worksheet of 20+ questions and answers. Includes reasoning and applied questions.

DOWNLOAD FREE

x

Two way tables worksheet

Get your free two way tables worksheet of 20+ questions and answers. Includes reasoning and applied questions.

DOWNLOAD FREE

Related lessons on representing data

Two way tables is part of our series of lessons to support revision on representing data. You may find it helpful to start with the main representing data lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:

Example 1: missing row and column totals

Complete this two way table,

Fill in the known values into the two way table.

Here, we know each of the individual values for each category so we can move on to Step 2.

2 Calculate missing values.

Here, we do not have any missing values and so we can move on to Step 3.

3 Calculate the row and column totals.

The total number of boys = 18 + 7 = 25 .

The total number of girls = 10 + 23 = 33 .

The total number of students who like rugby = 18 + 10 = 28 .

The total number of students who do not like rugby = 7 + 23 = 30 .

Filling in these values into the table, we have

4 Check the final total.

The total number of boys and girls = 25 + 33 = 58 .

The total number of students who do (not) like rugby = 28 + 30 = 58 .

Filling in the grand total of 58 , we have the final solution.

Example 2: three categories with missing totals

Complete this two way table,

Here, we know each of the individual values for each category so we can move on to Step 2.

Here, we do not have any missing values and so we can move on to Step 3.

Example 3: missing values throughout the table

Complete this two way table,

Here, we know some of the individual values for each category so we can move on to Step 2.

We have quite a few missing values in the two way table, so we need to find these values. We need to look for a row or column where we know all but one of the missing values.

Here, we know the number of females who can swim, and the total number of people who can swim. This means we can calculate the number of males by subtracting the number of females from the row total, 49-23 = 26.

Now we can calculate the number of males that cannot swim as we know the number of males that can swim, and the total number of males, 30-26 = 4 .

Now we can calculate the number of females who cannot swim, 31-4 = 27 .

The total number of females = 23 + 27 = 50 .

Filling in this value, we have

Example 4: constructing a two way table from a worded problem

A school is researching the handedness of 90 students in Year 3. 17 students in Class A are right-handed. 14 students in Class B are left-handed. 16 students in Class C are left-handed. There are 44 students who are right-handed, and 30 students in Class B. Construct a two way table to represent this data.

We have quite a few missing values in the two way table, so we need to find these values. We need to look for a row or column where we know all but one of the missing values.

Here, we know that out of the 30 students in Class B, 14 are left-handed, and so we can find the number of right-handed students in Class B, 30-14 = 16 .

We now know all but one value in the right-handed row, 44-(17 + 16) = 11 .

For the number of left-handed students in Class A, we need to know the row total, 90-44 = 46 .

The number of left-handed students in Class A = 46-(14 + 16) = 16 .

The total number of students in the three classes = 27 + 30 + 23 = 90 .

The total number of left-/right-handed people = 46 + 44 = 90 .

Example 5: using a two way table to work out a probability

160 students chose to study History or Geography.

86 of the students chose History.

34 of the boys chose Geography.

41 of the girls chose History.

A student is chosen at random. By constructing a two way table, work out the probability that the student is a boy who studies history.

The total number of boys = 45 + 34 = 79 .

The total number of girls = 41 + 40 = 81 .

Example 6: conditional probability

People can sit in a seat in the stalls or the circle or the balcony of a theatre. There are 150 seats altogether.

There are 60 children who have seats in the theatre.

There are 44 adults in the stalls and 23 adults in the circle.

Altogether there are 65 people in the stalls and 50 people in the balcony.

A person is chosen at random. Work out the probability that the person is a child, given that they are sitting on the balcony.

The only total we need to calculate to complete the two way table is the number of adults,

44+23+23 = 90 .

Common misconceptions

The numbers in the two way table are whole numbers, not decimals or fractions. This is because the numbers are frequencies where data has been counted.

The situations in maths questions have been simplified to make the situation simpler to study. The world is a more complex place to live. So individuals need to go under one category and one only.

For example, a school asks students to choose football or rugby. In maths we keep these separate. But in real-life the school may accommodate students who want to choose both or neither. This is where we would use a Venn diagram instead.

Step-by-step guide: Venn diagram

Each individual is only counted once in the main body of the table. Each of the 14 individuals are only in one of the four cells of the main section of the table.

Be careful not to double the overall total (or grand total).

For example, the 'grand total' of this table is 6 . Each individual item only counts once towards the 'grand total'. But it can be worked out using the row totals or the column totals.

4+2=3+3=6

Practice two way tables questions

Two way tables GCSE questions

1. Complete the two way table:
(3 marks)

6,1,3,13,7,15
(3)
5 correct
(2)
4 correct
(1)

2. 70 students each choose to study Drama or Music.

32 of the students choose Drama.
17 boys choose Music.
19 girls choose Drama.

(a) Use this information to complete the two way table.

(b) A student is picked at random. Work out the probability that the student is a boy who chooses drama.

(c) A Music student is picked at random. Work out the probability that the student is a girl.
(8 marks)

(a)
(1)
17, 19, 32, 70
(3)
3 correct
(2)
2 correct
(1)
(b)

13 or 70
(1)
\frac{13}{70}
(1)
(c)

17 or 38
(1)
\frac{17}{38}
(1)

3. 100 students are asked to choose one revision session to attend.

The revision classes are - Biology or Chemistry or Physics.

There are 53 male students.

45 students choose Physics.

13 female students choose Biology.

19 male students choose Chemistry and 17 choose Biology.

(a) Complete the two way table.

(b) How many female students choose Chemistry?

(c) A student is picked at random. Work out the probability that the student is male and choose physics.

(d) A Biology student is picked at random. Work out the probability that the student is Female.
(9 marks)

(a)

(1)

6, 28, 47, 17, 30, 25
(3)
5 correct
(2)
4 correct
(1)
(b)

6 female students choose Chemistry.
(1)
(c)

17 or 100
(1)
\frac{17}{100}
(1)
(d)

13 or 30
(1)
\frac{13}{30}
(1)

Learning checklist

You have now learned how to:

Still stuck?

Prepare your KS4 students for maths GCSEs success with Third Space Learning. Weekly online one to one GCSE maths revision lessons delivered by expert maths tutors.

Find out more about our GCSE maths tuition programme.

We use essential and non-essential cookies to improve the experience on our website. Please read our Cookies Policy for information on how we use cookies and how to manage or change your cookie settings. Accept

# data[].attributes.attachment_link.description
Free two way tables GCSE maths revision guide, including step by step examples, exam questions and free two way tables worksheet.