 |
| Image Credit: Pixabay.com |
Cumulative frequency
Cumulative frequency is defined as a running total of frequencies i.e., the sum of all previous frequencies up to the current point.↪ The cumulative frequency at a certain point is found by adding the frequency at the present point to the cumulative frequency of the previous point.
↪ Cumulative frequency can be used to determine the number of observations that lie below (or above) a particular value in a data set. This is very helpful in finding the median for large data.
↪ It is usually observed by constructing a cumulative frequency table.
↪ It is usually observed by constructing a cumulative frequency table.
Example - Data of marks, out of 50, obtained by 100 students in a test is arranged in a frequency table as below:
↪ The last value will always be equal to the total number of observations (Σf), since all frequencies will already have been added to the previous total.
Cumulative frequency distribution for grouped data
Cumulative frequency for a class is the number of observations that lie below (or above) of that particular class in a data set.↪ Cumulative frequency distribution of the less than type
The cumulative frequency for a class is the sum of frequencies less than the upper class limit and found by adding the frequency of the present class to the cumulative frequency of the previous class.
It increases as we move down the classes.
↪ Cumulative frequency distribution of the more than type
The cumulative frequency for a class is the sum of frequency more than or equal to the lower class limit and found by adding the frequency of the present class to the cumulative frequency of the next class. Or it can be found by subtracting the respective frequency from cumulative frequency of the previous class.
It decreases as we move down the classes.
Ex- A grouped frequency distribution of marks obtained, out of 100, by 53 students, in a certain examination, is as follows:
Cumulative Frequency Graph (Ogive)
A cumulative frequency graph, or an Ogive, is a curve showing the cumulative frequency for a given set of data.The term ‘ogive’ is pronounced as ‘ojeev’ and is derived from the word ogee. It has a shape of an elongated 'S' and is sometimes called a double curve with one portion being concave and the other being convex. In architecture, the ogee shape is one of the characteristics of the 14th and 15th century Gothic styles.
Ogive For ungrouped data
Variables and Cumulative frequencies are plotted on x-axis and y-axis on a suitable scales respectively. Data points(x, y) are plotted and joined to obtain the graph.Ogive for grouped data
Less than Ogive
Upper Class limits and Cumulative frequencies are plotted on x-axis and y-axis on a suitable scales respectively. Data points(x, y) are plotted and joined to obtain the graph.
More than Ogive
Lower Class limits and Cumulative frequencies are plotted on x-axis and y-axis on a suitable scales respectively. Data points(x, y) are plotted and joined to obtain the graph.
| Mode for Grouped Data | |