Use Frequency Tables

In this worksheet, students practise using frequency tables to collect and sort data

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR

Curriculum topic:   Statistics

Curriculum subtopic:   Statistics, Interpreting and Representing Data

Difficulty level:

QUESTION 1 of 10

In statistics, you frequently have to collect and analyse data. The vast majority of the times you do this, you will get a large amount of data that needs to be worked with which makes it almost impossible to deal with if you write it as a list.

To get round this, we use frequency tables.

What is a frequency table?

The word frequency just means 'how often something happens', so a frequency table is just a table that groups things together and tells you how often something happens.

Discrete and Continuous data.

In stats, there are two types of data. Discrete data and continuous data. For each type, we have to use a slightly different approach.

To put it simply.

Continuous data is something that could be broken down into smaller measurement (i.e. Height, whatever units you are using to measure it, there's always a smaller unit.

Discrete Data is something that can't be split down. (i.e. Hair colour, number of rooms in a house)

Example 1: I do a survey into the colour of cars and get the following colours.

Red, Blue, Blue, Red, Green, Blue, Red, Red, Blue, Green, Red, Black, Blue, Blue, Red, Green, Green, Red, Red, Blue, Green

Put the following data into a frequency table.

The first thing we need to do is create a table to put this data in, we need two columns. one for the category (in this case colour) and one for the frequency (how many times we get this colour).

 Colour Frequency Red Blue Green Black

We now need to count how many of each colour we have, this will give us the following, complete, frequency table.

 Colour Frequency Red 8 Blue 7 Green 5 Black 1

Example 2: I measure the heights of some children and get the following results (all given in centtimetres)

132, 145, 165, 133, 142, 147, 152, 161, 164, 131, 135, 137, 149, 148, 171, 140, 150

Put this data into a grouped frequency table.

This one is slightly different, we can't use exactly the same approach as before because all the numbers are different (This will usually happen if you are measuring something that can be measured on a scale i.e. Heights, Weights).

To deal with this, we use a grouped frequency table. The difference between this and a frequency table is that instead of having one thing for the category, we have a range.

 Height (cm) Frequency 130 < h ≤ 140 140 < h ≤ 150 150 < h ≤ 160 160 < h ≤ 170 170 < h ≤ 180

Lets take a couple as a examples,

the first number is 132, which would clearly go in the 130 < h ≤ 140 box.

The last number is 150, this you have to think about a bit more. 140 < h ≤ 150 means anything up to and including 150 where as  150 < h ≤ 160 means anything above 150. 150 would go in the 140 < h ≤ 150 box.

 Height (cm) Frequency 130 < h ≤ 140 6 140 < h ≤ 150 6 150 < h ≤ 160 1 160 < h ≤ 170 3 170 < h ≤ 180 1

We normally use a frequency table to...

Complete the following sentence...

We normally use a grouped frequency table to...

For each of these situations, select if you would use a frequency table or a grouped frequency table to record your results.

I record the hair colour of 10 people in the street and get the following values.

Red, Blonde, Blonde, Brown, Black, Brown, Red, Blonde, Blonde, Bald, Blonde, Brown, Brown,

Complete the frequency table.

 Frequency Red Blonde Brown Black Bald

I record the hair colour of 10 people in the street and get the following values.

Red, Blonde, Blonde, Brown, Black, Brown, Red, Blonde, Blonde, Bald, Blonde, Brown, Brown,

If someone else walks past me, which hair colours are they the least likely to have?

Red

Blonde

Brown

Black

Bald

These are the marks for 36 students in a maths exam.

31, 49, 52, 79, 40, 29, 66, 71, 73, 19, 51, 47

81, 67, 40, 52, 20, 84, 65, 73, 60, 54, 60, 59

25, 89, 21, 91, 84, 77, 18, 37, 55, 41, 72, 38

 Frequency 0 - 20 21 - 40 41 - 60 61 - 80 81 - 100

These are the marks for 36 students in a maths exam.

31, 49, 52, 79, 40, 29, 66, 71, 73, 19, 51, 47

81, 67, 40, 52, 20, 84, 65, 73, 60, 54, 60, 59

25, 89, 21, 91, 84, 77, 18, 37, 55, 41, 72, 38

Which group of scores are the students most likely to get

0 - 20

21 - 40

41 - 60

61 - 80

81 - 100

I roll a dice and record the results.

2, 4, 2, 6, 1, 5, 4, 3

3, 2, 3, 6, 2, 1, 3, 5,

4, 3, 4, 2, 1, 6, 5

1, 6, 4, 1, 2, 3, 4

Put this data into a frequency table

 Frequency 1 2 3 4 5 6

I roll a dice and record the results.

2, 4, 2, 6, 1, 5, 4, 3

3, 2, 3, 6, 2, 1, 3, 5,

4, 3, 4, 2, 1, 6, 5

1, 6, 4, 1, 2, 3, 4

How many times did I roll the dice?

I roll a dice and record the results.

2, 4, 2, 6, 1, 5, 4, 3

3, 2, 3, 6, 2, 1, 3, 5,

4, 3, 4, 2, 1, 6, 5

1, 6, 4, 1, 2, 3, 4

Do you think this dice is fair?

Yes

No

• Question 1

We normally use a frequency table to...

CORRECT ANSWER
EDDIE SAYS
A normal frequency table is great when you have something that is a single value and can't be split up into smaller units. We call this data discrete data.
• Question 2

Complete the following sentence...

We normally use a grouped frequency table to...

CORRECT ANSWER
EDDIE SAYS
Continuous data is recorded on a scale so it is likely that there will be no two values the same. To get round this we use a grouped frequency table
• Question 3

For each of these situations, select if you would use a frequency table or a grouped frequency table to record your results.

CORRECT ANSWER
EDDIE SAYS
To get this question right, you need to ask the question 'Can this be split into a smaller measurement?' If it can, use a grouped frequency table If it can't, use a frequency table
• Question 4

I record the hair colour of 10 people in the street and get the following values.

Red, Blonde, Blonde, Brown, Black, Brown, Red, Blonde, Blonde, Bald, Blonde, Brown, Brown,

Complete the frequency table.

CORRECT ANSWER
 Frequency Red Blonde Brown Black Bald
EDDIE SAYS
All you have to do here is count how many of each there are. Feel free to use tallies to do this if you want, just don\'t forget to change them into a frequency at the end
• Question 5

I record the hair colour of 10 people in the street and get the following values.

Red, Blonde, Blonde, Brown, Black, Brown, Red, Blonde, Blonde, Bald, Blonde, Brown, Brown,

If someone else walks past me, which hair colours are they the least likely to have?

CORRECT ANSWER
Black
Bald
EDDIE SAYS
We can assume that this pattern will be pretty similar for the next few people to walk past. I've seen only one bad person and one with black hair so they're the least likely I will see again
• Question 6

These are the marks for 36 students in a maths exam.

31, 49, 52, 79, 40, 29, 66, 71, 73, 19, 51, 47

81, 67, 40, 52, 20, 84, 65, 73, 60, 54, 60, 59

25, 89, 21, 91, 84, 77, 18, 37, 55, 41, 72, 38

CORRECT ANSWER
 Frequency 0 - 20 21 - 40 41 - 60 61 - 80 81 - 100
EDDIE SAYS
Even though you can\'t split the marks down (no half marks in this test), there are 36 different scores here so we have to use a grouped frequency table. All we\'re doing is working through and saying which of the rows each number has to go in.
• Question 7

These are the marks for 36 students in a maths exam.

31, 49, 52, 79, 40, 29, 66, 71, 73, 19, 51, 47

81, 67, 40, 52, 20, 84, 65, 73, 60, 54, 60, 59

25, 89, 21, 91, 84, 77, 18, 37, 55, 41, 72, 38

Which group of scores are the students most likely to get

CORRECT ANSWER
41 - 60
EDDIE SAYS
All we need to remember here is which of the rows from the last question had the highest frequency.
• Question 8

I roll a dice and record the results.

2, 4, 2, 6, 1, 5, 4, 3

3, 2, 3, 6, 2, 1, 3, 5,

4, 3, 4, 2, 1, 6, 5

1, 6, 4, 1, 2, 3, 4

Put this data into a frequency table

CORRECT ANSWER
 Frequency 1 2 3 4 5 6
EDDIE SAYS
A nice easy one here, we can\'t split the numbers on a dice and there are lots of repeated numbers so we use a frequency table. Count up the 1s, count up the 2s etc. Don\'t forget that frequency must be a number and not a tally.
• Question 9

I roll a dice and record the results.

2, 4, 2, 6, 1, 5, 4, 3

3, 2, 3, 6, 2, 1, 3, 5,

4, 3, 4, 2, 1, 6, 5

1, 6, 4, 1, 2, 3, 4

How many times did I roll the dice?

CORRECT ANSWER
30
EDDIE SAYS
This is usually a follow-up question when you've drawn the table. All you need to do here is add up the frequencies and that's your total!
• Question 10

I roll a dice and record the results.

2, 4, 2, 6, 1, 5, 4, 3

3, 2, 3, 6, 2, 1, 3, 5,

4, 3, 4, 2, 1, 6, 5

1, 6, 4, 1, 2, 3, 4

Do you think this dice is fair?

CORRECT ANSWER
Yes
EDDIE SAYS
This is a bit trickier, you have to explain why. If we throw a dice 30 times, we should get 5 of each number (or nearly that) Our frequency table shows that we do get close to 5 on all the numbers, so I'd say the dice was fair.
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