Frequency Distribution and Graphical Representation

When raw data is collected, it is usually unorganized and difficult to interpret. To make it meaningful, we arrange it into frequency distributions and display it using graphs.

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1. Frequency Distribution

A frequency distribution is a tabular arrangement of data showing how often (frequency) each value or group of values occurs.

It helps in:

• Summarizing large data
• Identifying patterns and trends
• Making the data easier to understand

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Types of Frequency Distributions

1.1. Ungrouped Frequency Distribution

Used for small datasets. Each value is listed along with its frequency.

Example: Marks: 2, 3, 3, 4, 5

Marks	Frequency
2	1
3	2
4	1
5	1

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1.2. Grouped Frequency Distribution

Used for large datasets. Data is divided into class intervals (groups). Each interval has a frequency.

Example:

Class Interval	Frequency
0 – 10	5
10 – 20	8
20 – 30	12

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1.3. Cumulative Frequency Distribution

Shows the running total of frequencies.

Types:

• Less than cumulative frequency
• More than cumulative frequency

Used for OGIVE curves.

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2. Graphical Representation

Graphs help visualize patterns and make comparisons quickly.

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2.1. Histogram

• A bar graph for continuous (grouped) data
• Bars are adjacent (no gaps)
• Height of bar = frequency

Used for: distribution of marks, heights, weights.

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2.2. Frequency Polygon

• Formed by joining the midpoints of histogram bars with straight lines
• Can be drawn with or without a histogram
• Shows the shape of the distribution

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2.3. Ogive (Cumulative Frequency Curve)

Two types:

1. Less than Ogive
2. More than Ogive

Used to find:

• Median
• Percentiles
• Quartiles

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2.4. Bar Chart

• For categorical (qualitative) data
• Bars have gaps between them
• Height = frequency of the category

Examples: number of students in different classes

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2.5. Pie Chart

• Circular chart divided into sectors
• Each sector represents a proportion of the whole
• Useful for showing percentages or parts of a whole

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2.6. Line Graph

• Used to show changes over time
• Points connected by straight lines
• Example: yearly sales, monthly temperature

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3. Difference Between Histogram and Bar Chart

Histogram	Bar Chart
For continuous data	For categorical data
No gaps between bars	Gaps between bars
Shows distribution shape	Shows category comparisons

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Conclusion

Frequency distribution organizes data into meaningful form, while graphs like histograms, polygons, and pie charts help visualize and understand data patterns easily.

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