Cumulative Frequency

Understanding Cumulative Frequency

• Cumulative frequency is the running total of frequencies.
• This procedure involves the sum of all frequencies up to a certain point in a frequency distribution.
• Cumulative frequency is often used to create a cumulative frequency curve, often termed an ogive, which can help in visualising the distribution of data.

Constructing a Cumulative Frequency Table

• Start with a frequency table containing data groups or intervals and their corresponding frequencies.
• A row for cumulative frequency is created. The first cumulative frequency is simply the first frequency.
• For every subsequent entry in the cumulative frequency row, the current frequency is added to the previous cumulative frequency.

Constructing a Cumulative Frequency Graph (Ogive)

• An ogive is a line graph, therefore, it requires an X-Y axis.
• The class limits or intervals go on the x-axis and the cumulative frequencies go on the y-axis.
• Points are plotted at the end of each interval. A point’s x-coordinate is the upper class limit of an interval and its y-coordinate is the corresponding cumulative frequency.
• After plotting the points, they are connected with a smooth curve.

Understanding and Interpreting Ogives

• An ogive is useful to understand the overall trend of data, it’s upper and lower limits and the spread of the data.
• The curve gives a good visual picture of the cumulative distribution of the data.
• Unlike a histogram, an ogive doesn’t have bars but a curve that rises from left to right.
• The steeper sections of the curve represent intervals with higher frequencies, while flatter sections represent lower frequencies.

Applications of Cumulative Frequency and Ogives

• They are particularly useful in predicting the number of observations that lie above or below a particular value in a dataset.
• Cumulative frequency analysis is valuable in comparing different data sets.
• It can be used to identify percentiles, quartiles and the median in a set of observations.
• These can be very helpful in situations where one wishes to see how the frequencies accumulate over the categories or to compare two or more frequency distributions.