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Frequency, Frequency Tables and Levels of Measurement

Frequency, Frequency Tables and Levels of Measurement

Have you ever wondered how your teacher may keep track of the results from a test? Or maybe how they may record the information to find out the most common results? When data is collected it can be useful to sort it and display it in a way that is easy to read. This is sometimes known as a way of representing data. One way of representing data is through a frequency table.

Frequency is a term that describes the number of times a value occurs in a collection of data.

Frequency tables definition

A frequency table is a type of table used to represent the different frequencies from a collection of data.

Steve flips a coin 5 times to find out whether it will land showing heads or tails. He records the results of each flip in a table.

Flip
Heads or Tails
1
Heads
2
Tails
3
Heads
4
Tails
5
Tails

Steve flips the coin another 5 times.

Flip
Heads or Tails
1
Heads
2
Tails
3
Heads
4
Heads
5
Heads

We can now place the results from both tests into one frequency table:

Heads or TailsTally Frequency
Heads
6
Tails
4

This tells us that out of the 10 coin tosses Steve made, 6 landed with heads facing up and 4 with tails facing up.

Frequency table examples

A frequency table can be useful when you have a large amount of data, this is because it groups the data into groups making it easier to understand.

A frequency table can look like this:

VariableTallyFrequency
1 - 55
6 - 103
11 - 157

How to create a frequency table

In order to create a frequency table, you must first look at your data and create suitable groups. Your group size may depend on the number of variables you have. Once you have grouped your data you can tally the number of times each variable occurs to find out the frequency. Let's have a look at an example:

A year 7 class has completed a maths test. The results, as a percentage, from the 25 students have been recorded below:

6373394582
28
77643547
9257855362
6659469182
7446284690

In order to put this into a frequency table, you first need to find the group sizes, the smallest variable is 28 and the biggest variable is 92. This data could be split into 7 groups:

Test Results (%)
25 - 35
36 - 45
46 - 55
56 - 65
66 - 75
76 - 85
86 - 95

Now you can go through the data and mark a tally where the variables fall into each group:

Test Results (%)
Tally
25 - 35
36 - 45
46 - 55
56 - 65
66 - 75
76 - 85
86 - 95

Finally, you can add the next column, the frequency for each of the groups:

Test Results (%)TallyFrequency
25 - 35
3
36 - 45
2
46 - 55
5
56 - 65
5
66 - 75
3
76 - 85
4
86 - 95
3

From this frequency table, you can now understand the data much easier. Just by taking a quick look, you can easily see that 5 students scored between 46% and 55% on the maths test.

Sometimes, there may only be a small amount of variables, if this is the case there may not be a need to group them. For example, if you are looking at the number of siblings people have and the variables range from 0 - 4, you could just look at each variable separately.

A group of students records the number of cups of coffee they drink per day. The results are shown below:

23610
34223
51142
73251

To put this into a frequency table, you first need to find the group sizes, the smallest variable is 0 and the biggest variable is 6:

Number of coffees
0-1
2-3
4-5
6-7
Now you can through the data and mark a tally where the variables fall into each group:
Number of coffeesTally
0-1
2-3
4-5
6-7

Finally, you can add the next column, the frequency for each of the groups:

Number of Coffees
Tally
Frequency
0-1
5
2-3
9
4-5
4
6-7
2

By creating this frequency table you can now much easier read that the most common amount of coffees that a group of students drinks in a day is between 2 and 3.

Level of measurement in statistics

The level of measurement tells you how data is recorded. There are four different levels of measurements used in statistics:

  • Nominal
  • Ordinal
  • Interval
  • Ratio

Nominal

The nominal level of measurement is data that can be categorised but the data has no order.

Place of birth, eye colour, gender.

Ordinal

The ordinal level of measurement is data that can be categorised and ordered. Although there is an order between the data, you cannot see the intervals between each variable.

Satisfaction survey, top 5 goal scorers.

Interval

The interval level of measurement is data that can be categorised and ranked and there is a scale on which you know the difference between each of the variables.

Temperature, test scores.

Ratio

The ratio level of measurement gives an order to the variables, where there is a difference between the variables, as well as a true zero point.

Height, age.

The true zero indicates that there is an absence of something on the scale.

Level of Measurement Examples

Data is taken from a class to find out the most common hair colour. The results collected can be considered as the nominal level of measurement since the data can be categorised.

The weights of different piles of sugar are recorded. One result shows 0 kg. This can be considered the ratio level of measurement since there is a chance of a true zero within the results.

A group of people is asked what their highest level of education is. The results collected from this can be considered as the ordinal level of measurement since they can be categorised and ordered.

The temperature is recorded over a period of a week. When these results are collected the data can be considered as the interval level of measurement since the temperature has evenly spaced intervals.

Frequency, Frequency Tables and Levels of Measurement - Key takeaways

  • Frequency tables can be used to display data and help to easily understand data.
  • To create a frequency table you must first group your data, before tallying up the amount of variables that fall into each group.
  • There are four levels of measurement:
    • Nominal
    • Ordinal
    • Interval
    • Ratio

Frequently Asked Questions about Frequency, Frequency Tables and Levels of Measurement

A frequency table is a way of representing a collection of data. 

To create a frequency table you start by grouping the variables before counting the amount of times the data falls into each of the groups and finding the frequency. 

  • Nominal
  • Ordinal
  • Interval 
  • Ratio

To calculate the frequency of the data, you can use a frequency table. First you group the data before tallying the amount of variables that fall into each group. 

There are two types of frequency tables; grouped data and ungrouped data frequency tables. 

Final Frequency, Frequency Tables and Levels of Measurement Quiz

Question

What is frequency?

Show answer

Answer

Frequency is a term that describes the number of times a value occurs in a collection of data. 

Show question

Question

What is a frequency table?

Show answer

Answer

A frequency table is a type of table used to represent the different frequencies from a collection of data. 

Show question

Question

How do you create a frequency table?

Show answer

Answer

To create a frequency table you must first group your data into suitable group sizes. You can then tally the number of times each variable occurs to find out the frequency.

Show question

Question

What are the four levels of measurement?

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Answer

  • Nominal 
  • Ordinal 
  • Interval 
  • Ratio

Show question

Question

What is the nominal level of measurement?

Show answer

Answer

The nominal level of measurement is data that can be categorised but the data has no order. 

Show question

Question

What is the ordinal level of measurement?

Show answer

Answer

The ordinal level of measurement is data that can be categorised and ordered. However, you cannot see the intervals between the variables. 

Show question

Question

What is the interval level of measurement?

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Answer

The interval level of measurement is data that can be categorised, ranked and there is a scale in which you know the difference between each of the variables. 

Show question

Question

What is the ratio level of measurement?

Show answer

Answer

The ratio level of measurement gives an order to the variables, where there is a difference between the variables, as well as a true zero point. 

Show question

Question

What does the term true zero mean?

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Answer

The true zero indicates that there is an absence of something on the scale. 

Show question

Question

A group of year 10 students run a 100 m race, the times in seconds are recorded below. Create a frequency table to find out how many students ran the race in under 40 seconds.


34, 56, 23, 21, 44, 23, 54, 23, 45, 43, 37, 27, 45, 34, 67, 29, 58, 41, 36, 31, 47, 39

Show answer

Answer

12 students ran the race in under 40 seconds. 

Show question

Question

After an easter egg hunt, the participants counted how many eggs they had found. The amount of eggs each person found was recorded below. Create a frequency table to help you find out how many people found 7 or more eggs. 


3, 5, 2, 7, 10, 8, 11, 5, 6, 2, 9, 1, 5, 8, 3, 6, 10, 13, 4, 1, 6, 3, 8, 9, 4, 7, 8, 3  

Show answer

Answer

12 people found 7 or more eggs in the hunt. 

Show question

Question

What are the benefits of a frequency table?

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Answer

When you have a big collection of data, putting it into a frequency table can make it easier to understand and interpret.  

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Question

What are some examples of nominal levels of measurement?

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Answer

Place of birth, eye colour, gender. 

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Question

What are some examples of interval levels of measurement?

Show answer

Answer

Temperature, time, test scores 

Show question

Question

What are some examples of ratio levels of measurement?


Show answer

Answer

Height, age. 

Show question

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