Frequency Distribution

Frequency Distribution Psychology Definition

Fg. 1 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.

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:

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

Frequency distributions also include cumulative relative frequencies.

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.

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

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.

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.

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.

Fg. 2 A 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.

Fg. 3 A 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).

Fg. 4 A 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.

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

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.

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.