It provides a concise overview of the data set’s distribution and helps in understanding patterns and trends. There are several types of frequency distributions, each serving different purposes depending on the nature of the data. Here are the main types:
1. Simple Frequency Distribution
Definition: A simple frequency distribution lists each unique value or category of a variable and the number of times it occurs.
Example: For a dataset of test scores, a simple frequency distribution might list each score and the number of students who received that score.
Score
Frequency
85
5
90
8
95
12
100
7
2. Grouped Frequency Distribution
Definition: When data is continuous or has a large range, it is often grouped into intervals (or bins) to simplify the distribution. Each interval shows the number of data points that fall within that range.
Example: For a dataset of ages, ages might be grouped into intervals like 0-10, 11-20, etc.
Age Interval
Frequency
0-10
15
11-20
25
21-30
20
31-40
10
3. Cumulative Frequency Distribution
Definition: This type of distribution shows the cumulative frequency of data up to and including each interval or value. It helps to understand how data accumulates over intervals.
Example: Using the grouped frequency distribution of ages, the cumulative frequency distribution would add up the frequencies from each interval.
Age Interval
Frequency
Cumulative Frequency
0-10
15
15
11-20
25
40
21-30
20
60
31-40
10
70
4. Relative Frequency Distribution
Definition: This distribution expresses the frequency of each value or interval as a proportion or percentage of the total number of data points. It is useful for comparing distributions between different datasets.
Example: For the simple frequency distribution of test scores, relative frequencies can show the proportion of students who scored each value.
Score
Frequency
Relative Frequency
85
5
5/32 ≈ 0.156 (15.6%)
90
8
8/32 ≈ 0.250 (25.0%)
95
12
12/32 ≈ 0.375 (37.5%)
100
7
7/32 ≈ 0.219 (21.9%)
5. Percentage Frequency Distribution
Definition: Similar to relative frequency distribution, this shows the frequency of each value or interval as a percentage of the total. It provides a more intuitive understanding of the proportion of each category.
Example: For a dataset of customer satisfaction ratings, percentage frequencies show how satisfied each percentage of customers is.
Rating
Frequency
Percentage Frequency
Poor
10
10%
Fair
30
30%
Good
40
40%
Excellent
20
20%
6. Frequency Polygon
Definition: A graphical representation of a frequency distribution, where the frequencies of each interval are plotted as points and connected by lines. It helps visualize the distribution of data.
Example: Using the grouped frequency distribution of ages, a frequency polygon would be created by plotting the midpoints of the intervals against their frequencies and connecting these points with lines.
7. Histogram
Definition: A bar chart that represents the frequency of data points within each interval of a grouped frequency distribution. The height of each bar corresponds to the frequency of that interval.
Example: For the age intervals, a histogram would have bars for each age range, with heights proportional to the frequency of each interval.
8. Ogive
Definition: A cumulative frequency graph that plots the cumulative frequencies against the upper boundaries of intervals. It helps in understanding the cumulative distribution of data.
Example: Using the cumulative frequency distribution of ages, an ogive would be plotted by marking cumulative frequencies on the vertical axis and age intervals on the horizontal axis.
Summary
Different types of frequency distributions—simple, grouped, cumulative, relative, and percentage—provide various ways to summarize and analyze data. Graphical representations like histograms, frequency polygons, and ogives enhance the understanding of data distributions. Choosing the appropriate type depends on the nature of the data and the specific analysis goals.