A frequency distribution is a systematic arrangement of data that shows how often each value (or group of values) occurs in a dataset. It helps organize raw data into a more understandable form, making it easier to see patterns, trends, and outliers.
In simple terms, frequency distribution tells us "how many times" a particular value or group of values appears in a dataset.
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Types of Frequency Distribution
1. Ungrouped Frequency Distribution
Used when data is small and consists of distinct, individual values.
Each value is listed along with the number of times it occurs (its frequency).
Example:
Marks: 10 12 15 18
Frequency: 3 5 6 2
2. Grouped Frequency Distribution
Used for large datasets where values are grouped into class intervals (e.g., 0–10, 10–20).
It helps simplify and summarize large data sets.
Example:
Marks Range: 0–10 10–20 20–30
Frequency: 2 6 5
3. Cumulative Frequency Distribution
Shows the cumulative total of frequencies up to each class.
Two types:
Less Than Cumulative Frequency – Cumulative totals from the start.
More Than Cumulative Frequency – Cumulative totals from the end.
4. Relative Frequency Distribution
Shows frequencies as proportions or percentages of the total.
Useful for comparing distributions with different total frequencies.
5. Bivariate Frequency Distribution
Involves two variables (e.g., height and weight).
Used in correlation and regression analysis.
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Construction Method of Frequency Distribution
Step-by-Step Process:
1. Collect Raw Data – Start with unorganized numerical data.
2. Determine the Range – Subtract the smallest value from the largest.
3. Decide Number of Classes – Usually 5 to 20 classes depending on data size.
4. Calculate Class Width –
\text{Class Width} = \frac{\text{Range}}{\text{Number of Classes}}
6. Tally Frequencies – Count how many data points fall in each interval.
7. Create the Table – List class intervals with their corresponding frequencies.
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Graphical Representation of Frequency Distribution
1. Histogram
A bar graph for grouped data.
Bars touch each other, showing continuous data intervals.
Height of bar = frequency.
2. Frequency Polygon
Line graph created by plotting midpoints of class intervals vs frequency.
Points are connected with straight lines.
3. Ogive (Cumulative Frequency Curve)
Two types:
Less than Ogive
More than Ogive
Used to find median and percentiles.
4. Bar Chart
Used for ungrouped or categorical data.
Bars do not touch each other.
5. Pie Chart
Represents relative frequency distribution as circular sectors.
Good for visualizing proportions.
6. Line Graph
Shows frequency trends over time or categories.
Commonly used in time series data.
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Conclusion
A frequency distribution is essential for organizing and analyzing data in a systematic way. It allows statisticians, researchers, and business professionals to interpret large datasets clearly. With the help of tables and graphs like histograms and polygons, data becomes visually accessible and meaningful for further analysis and decision-making.
