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Frequency Distribution

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Frequency Distribution

Researchers get a lot of information in the form of measurements and scores. The question is, how should this data be organized for better understanding? This is where frequency distribution, a technique for managing data used in descriptive statistics, comes in handy.

  • What is frequency distribution in psychology?

  • What are the three types of frequency distribution?

  • What are the four types of data and their frequency distribution graphs?

  • What is an example of frequency distribution in psychology?

  • What is cumulative frequency distribution in psychology?

Frequency Distribution Psychology Definition

A frequency distribution: Also known as a frequency table, a frequency distribution is a visual depiction of the frequency of certain events in a particular set of values.

Frequency Distribution, Depiction of 5-point rating, pexels.com, StudySmarter Depiction of 5-point rating, Pexels.

Here is a list of scores from a 5-point rating scale:

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

Let's summarize these scores in a frequency distribution. In the frequency distribution table, make two columns. Label the left column, X, representing the scores, and the right column, f, representing the frequency.

To get the frequency in the frequency distribution table, arrange the scores in ascending or descending order on the left, then enter the frequency of each score on the right.

X
f
5
7
4
4
3
6
2
2
1
1

Frequency distribution gives a clear picture of the distribution of values. By organizing data in a distribution table, researchers can identify impossible values and the location of scores in a distribution. A frequency distribution shows how high or low measurements are.

Types of Frequency Distributions

There are three types of frequency distribution:

  • Categorical frequency distribution.
  • Grouped frequency distribution.
  • Ungrouped frequency distribution.

Categorical frequency distribution

Categorical frequency distribution is the distribution frequency of classifiable values such as blood type or educational level.

Here is an example of a categorical frequency distribution table:

X = Blood type
f
Relative frequency
A
7
0.35 or 35%
B
4
0.20 or 20%
AB
6
0.30 or 30%
O
2
0.10 or 10%
A+
1
0.05 or 5%

In a frequency distribution, researchers can also compute relative frequencies.

Relative frequency: shows how often a score occurs within total frequencies in a distribution table. To get the relative frequency of a score in a frequency distribution, divide a score's frequency by the total number of frequencies.

To find the relative frequency of the first row, divide 7 by 20 (the total number of outcomes), which is equal to 0.35 or 35%.

Frequency distributions also include cumulative relative frequencies.

Cumulative relative frequency: the sum of prior relative frequencies in a distribution table. To find the cumulative relative frequency of a score in distribution frequency, combine its relative frequency with all relative frequencies above it.

X = Blood type
f
Relative frequency
Cumulative relative frequency
A
7
0.35 or 35%
0.35
B
4
0.20 or 20%
0.35 + 0.20 = 0.55
AB
6
0.30 or 30%
0.55 + 0.30 = 0.85
O
2
0.10 or 10%
0.85 + 0.10 = 0.95
A+
1
0.05 or 5%
0.95 + 0.05 = 1.00

Grouped frequency distribution

Grouped frequency distribution is the distribution frequency of grouped data called class intervals which appear as number ranges in a distribution table. Grouped frequency distributions are ideal for large amounts of data.

Here are a few guidelines for the distribution frequency of grouped data:

  • Generally, grouped frequency distributions should have at least 10 class intervals.
  • Ensure that a class interval width is a simple number.
  • The bottom score of each score range should be a multiple of the width.
  • A score should only belong in one class interval.

A Math teacher listed the grades of her 25 students as follows:

98, 90, 84, 92, 76, 87, 95, 83, 79, 80, 91, 94, 88, 75, 85, 84, 79, 96, 81, 75, 82, 89, 93, 97, 90

Let's organize these grades in a frequency distribution. The highest score (H) is 98, and the lowest score (L) is 75.

To identify the number of rows for the frequency distribution, use the following formula: H - L = difference + 1

98 - 75 = 23 + 1 (24 rows)

Twenty-four rows are too many, so we group the scores. With three as the interval width, there will be a total of 8 intervals in the frequency distribution (24/3 = 8). An interval width of 3 indicates three values for each interval.

75 (lowest score) = 75, 76, 77

Class interval: 75–77

X
f
9698
3
9395
3
9092
4
8789
3
8486
3
8183
3
7880
3
7577
3

Ungrouped frequency distribution

Ungrouped frequency distribution is the distribution frequency of ungrouped data listed as individual values in a distribution table. This type of frequency distribution is ideal for a small set of values.

X
f
7
1
6
2
5
1
4
3
3
2
2
4
1
3

In this frequency distribution, X represents the number of children in a household, and f is the number of families with said number of children. Here, we can see that four homes have two children, and one has seven children.

Frequency Distribution Graph

A frequency distribution graph illustrates available data in a frequency distribution. There are three types of frequency distribution graphs:

  • Histograms.
  • Polygons.
  • Bar graphs.

Generally, a frequency distribution graph consists of an X-axis (horizontal line) that contains the categories or set of scores arranged in increasing order from left to right. The Y-axis (vertical line) includes the frequencies decreasing from top to bottom.

Frequency Distribution, A picture of graphs, tables and chart representing data, pexels.com, StudySmarter Graphs, tables, and charts representing data, Pexels.

Types of Data

There are four types of data according to the measurement of scores in statistics:

  • Nominal data
  • Ordinal data
  • Interval data
  • Ratio data

Nominal (categorical) data: These are values that only represent labels or categories such as nationality, marital status, or dog breeds.

Ordinal (rank) data: These are values that can be arranged in an order, such as economic status, satisfaction ratings, and sports team rankings.

Nominal and ordinal (qualitative) data use a bar graph.

Interval data: These are values similar to ordinal data with equal intervals between values but no true zero point, such as Celsius or Fahrenheit, IQ scores, or calendar dates.

Ratio data: These are values similar to interval data but with a true zero point, such as weight, height, and blood pressure.

Interval and ratio data (quantitative) use a histogram or polygon.

Types of Frequency Distribution Graph

Aside from tabular representations, graphs also come in handy in displaying frequency distribution. Graphs allow easier interpretation of data than in tabular format. Numerical data graphically presented helps describe data and show any unnoticed patterns.

Histograms

Histograms display frequency distribution in a bar graph. The horizontal line shows the categories, and the vertical line indicates the frequencies. The bars touch because the bar width extends up to the midpoint between the next category.

Frequency Distribution, A Sample frequency histogram of maths grade, StudySmarterA sample frequency histogram of Math grades, StudySmarter Original

Polygons

A polygon is a line graph connecting points by a single line that pictures frequency distribution. Polygons help to display the shape of frequency distribution.

Frequency Distribution, A sample frequency polygon of Math grades, StudySmarterA sample frequency polygon of Math grades, StudySmarter Original

Bar graphs

Bar graphs present a distribution frequency similar to a histogram but with spaces between bars. Spaces indicate distinct categories (nominal data) or category sizes (ordinal data).

Frequency Distribution, A sample bar graph of marital status, StudySmarterA sample bar graph of marital status, StudySmarter Original

Frequency Distribution Psychology Example

Psychologists use frequency distributions to make sense of the data collected in their research. Frequency distributions allow them to see the bigger picture of the data. That is, they can detect any patterns unnoticed within the frequency distribution.

An example of frequency distribution in psychology is measuring attitudes or opinions using a Thurstone scale. Scores are summarized in a distribution table to understand behaviors and preferences better.

Thurstone scale: Named after L.L. Thurstone, a Thurstone Scale is a scale that measures respondents' opinions and attitudes. Researchers provide a list of agree-disagree statements assigned with a specific number to calculate the participants' responses. This method allows for making statistical comparisons.

X
f
11
8
10
5
9
3
8
2
7
1
6
3
5
3
4
2
3
5
2
2
1
1

In this table, X represents the statement, "Gardening helps relieve stress." A high score (11) indicates agreement with the idea, and a low (1) indicates disagreement. This frequency distribution shows that eight people agree that gardening helps them with stress, and only one disagrees.

Cumulative Frequency Distribution Psychology

Cumulative frequency: the sum of a class's frequency and the previous frequencies in a frequency distribution.

A cumulative frequency distribution shows the cumulative frequency of each class. Both grouped and ungrouped data use this type of frequency distribution. Researchers can use this frequency distribution in calculating the frequency up to a specific level.

X
f
Cumulative frequency
1940
3
3
1950
4
3+4=7
1960
8
7+8=15
1970
9
15+9=24
1980
12
24+12=36

This frequency distribution table shows how many people were born from the 1940s to the 1980s. To get the cumulative frequency of a row, add the current row's frequency to the frequencies before it.

Frequency Distribution - Key takeaways

  • Frequency distribution gives a full view of data that helps researchers make sense of the scores or measurements in terms of trends, patterns, location, and errors.

  • Two essential elements of a frequency distribution are the categories or intervals and the frequency or number of entries of each interval.

  • A frequency distribution graph depicts the set of values in a frequency distribution.

  • In dealing with large amounts of data, grouping scores into class intervals is beneficial.

  • Cumulative frequencies indicate the total frequencies to a certain level.

Frequently Asked Questions about Frequency Distribution

A frequency distribution, also known as a frequency table, is a visual depiction of the frequency of certain events in a particular set of values.

Frequency distribution gives a clear picture of the distribution of values. By organizing data in a distribution table, researchers can identify impossible values and the location of scores in a distribution. A frequency distribution shows how high or low measurements are.

There are three types of frequency distribution:

  • Categorical frequency distribution
  • Grouped frequency distribution
  • Ungrouped frequency distribution 

To get the frequency in the frequency distribution table, arrange the scores in ascending or descending order on the left, then enter the frequency of each score on the right.

Final Frequency Distribution Quiz

Question

Grouped frequency distributions should have at least ten intervals.

Show answer

Answer

True

Show question

Question

A grouped frequency distribution table with an interval width of 5, and the lowest score in the distribution is X = 29. What should be the bottom interval in the table?

Show answer

Answer

25-29

Show question

Question

A ________ is appropriate for interval or ratio data.


Show answer

Answer

Either histogram or polygon

Show question

Question

Which is an example of nominal data?


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Answer

Nationality

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Question

Arranging scores in a frequency distribution table:

Show answer

Answer

It gives a clear picture of the distribution of values

Show question

Question

The X in a frequency table represents the categories or set of values.


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Answer

True

Show question

Question

What should a researcher do if the scores require 50 rows in a frequency distribution table?


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Answer

Organize it into a grouped frequency distribution

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Question

A frequency table shows where X = 20 with a frequency of 4, and the total frequency of the table is 30. What is the relative frequency of this row?


Show answer

Answer

0.13

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Question

The Y-axis of a frequency table represents the:


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Answer

Frequencies

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Question

The difference between a histogram and a bar graph is that a histogram:


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Answer

It doesn’t have spaces between bars

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Question

________ is a visual depiction of the frequency of certain events in a particular set of values.


Show answer

Answer

Frequency distribution

Show question

Question

A frequency table can display relative frequencies as percentages, fractions, or decimals.


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Answer

True

Show question

60%

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