A graphical presentation of frequency distribution is a visual representation of data that shows the frequency of each category or interval of values within a dataset.
This is often done using bar charts, histograms, or pie charts, depending on the nature of the data.
Let's discuss each type with an example and include diagrams for better understanding.
1. Histogram
A histogram is used to display the frequency distribution of continuous or interval data.
It consists of contiguous (touching) bars. Each bar's height represents the frequency of data within each interval.
Example:
Let's say we have the test scores of 30 students as follows:
55, 60, 65, 70, 75, 75, 80, 80, 80, 85, 85, 85, 85, 90, 90, 90, 90, 90, 95, 95, 95, 100, 100, 100, 105, 110, 115, 120, 125, 130
We can create intervals such as 55-74, 75-94, 95-114, and 115-134. The histogram will display these intervals on the X-axis, and the frequency (number of scores) within each interval on the Y-axis.
Let's generate a histogram to visualize this data.
2. Bar Chart
A bar chart is similar to a histogram but is used for categorical data. Each bar represents a category, and its height represents the frequency of the category.
Example:
Consider the favorite fruit of 30 people, categorized as follows: Apples (10), Bananas (5), Cherries (8), and Dates (7).
In this case, each fruit type represents a category, and we can use a bar chart to show the frequency of each fruit preference among the group.
Let's also create a bar chart to illustrate this example.
3. Pie Chart
A pie chart represents data in a circular graph where each slice of the pie corresponds to a category, and the size of each slice is proportional to the frequency or percentage of the category within the dataset.
Example:
Using the same favourite fruit data: Apples (10), Bananas (5), Cherries (8), and Dates (7).
A pie chart would show each fruit as a slice of the pie, with the size of each slice representing the proportion of people who prefer that fruit.
We'll generate a pie chart to visualize this data.
4. Frequency Polygon
A frequency polygon is a graph that displays the frequencies of different data classes.
It's similar to a histogram but uses points connected by straight lines.
It's often used to compare the distributions of different datasets.
Example:
Let's say we have the test scores of 30 students as follows:
55, 60, 65, 70, 75, 75, 80, 80, 80, 85, 85, 85, 85, 90, 90, 90, 90, 90, 95, 95, 95, 100, 100, 100, 105, 110, 115, 120, 125, 130
5. Line Graph
A line graph is used to display information as a series of data points connected by straight line segments. It's commonly used to visualize data that changes over time.
Example:
For this, we'll use monthly sales data for a year: January (100), February (150), March (130), April (170), May (160), June (180), July (200), August (220), September (190), October (210), November (230), December (240).
6. Cumulative Frequency Curve (or Ogive)
A cumulative frequency curve, also known as an ogive, shows the cumulative frequency of data points up to a certain value. It's useful for understanding the distribution and quartiles of a dataset.
Example:
Let's say we have the test scores of 30 students as follows:
55, 60, 65, 70, 75, 75, 80, 80, 80, 85, 85, 85, 85, 90, 90, 90, 90, 90, 95, 95, 95, 100, 100, 100, 105, 110, 115, 120, 125, 130
