Which of the following graphs can be used for the representation of a cumulative frequency distribution? 

Key Points 

• The graph that can be used for the representation of a cumulative frequency distribution is the Ogive curve.
• An Ogive curve, also known as a cumulative frequency curve or an "S" curve, is constructed by plotting the cumulative frequencies against the upper boundaries of the class intervals in a frequency distribution. The cumulative frequency represents the total frequency up to a particular class or data point.
• By plotting the cumulative frequencies, an Ogive curve provides a visual representation of how the cumulative frequencies accumulate or increase as we move along the data values. It allows us to analyze the cumulative distribution and observe patterns such as the relative concentration of data points and the steepness of the curve.
• Ogive curves are particularly useful in analyzing and interpreting cumulative frequency distributions, as they help us understand the distribution of data and make comparisons between different datasets or subgroups within a dataset.

Additional Information

• Less than Ogive: A less than Ogive, also known as a cumulative frequency curve for values less than a given class boundary, represents the cumulative frequencies up to each class boundary. It plots the cumulative frequency against the upper boundaries of the class intervals. The curve shows how the cumulative frequency increases as we move from the lower values towards the upper values of the data.
• More than Ogive: A more than Ogive, also known as a cumulative frequency curve for values more than a given class boundary, represents the cumulative frequencies from each class boundary onwards. It plots the cumulative frequency against the lower boundaries of the class intervals. The curve illustrates how the cumulative frequency increases as we move from the higher values towards the lower values of the data.

• Both less than ogive and more than ogive provide visual representations of cumulative frequency distributions, allowing for the analysis of how frequencies accumulate in datasets.
• The median derived from ogives is the value corresponding to the point where the ogive curve intersects the cumulative frequency of 50%, indicating the middle point of the data distribution.
• These curves assist in understanding the overall distribution and characteristics of the data, such as the concentration of values and the shape of the cumulative distribution.

Hence, ogive curves can be used as the representation of a cumulative frequency distribution.