subject: Cumulative Frequency Ogive [print this page] An ogive is basically a shape of either a two dimensional or a three dimensional object, where it is roundly tapered at the end.
Ogive in Statistics.Ogive may be expressed using a single line. It is a cumulative line graph . The relative slopes from point to point will indicate greater or lesser increases.
For example At a time we are interested in knowing how many workers of a factory earn less than Rs. 400 per month or how many workers earn more than Rs. 2,000 per month, percentage of students who have failed in board exam, cricket score between two teams at a particular score with particular time interval etc. To answer these questions it is necessary to add the frequencies. When frequencies are added they are called cumulative frequencies. Then a table of cumulative frequencies is drawn, which when plotted on a graph paper is called the cumulative frequency curve or more popularly known as 'Ogive'.
The cumulative frequency, also known as an Ogive, is another way to analyze the frequency distribution table. Unlike a frequency distribution which tells you how many data points are with in each class, a cumulative frequency tells you how many are less than or within each of the class limits.There are two methods of constructing ogives:
Less than Method: In the less than method we start with upper limits of class and go on adding the frequencies. When these frequencies are plotted we get a rising curve.
An ogive, however, is not the ideal graphic for showing comparisons between categories because it simply combines the values in each category and thus indicates an accumulation, a growing or lessening total.If you want to keep track of a total and your individual values are periodically combined, it is the apt method to displace.It is useful for analyses that require quick results about the proportion of data that lies below a certain level.
Cumulative Frequency and Ogive
Terms to know before plotting Cumulative Frequency Ogive
Raw Data: The data in its original form is called raw data.
Frequency Distribution: The organizing of raw data in a tabular format using classes and frequencies.
Categorical Frequency Distribution: For data that can be placed in specific categories. For example, blood groups.
Grouped Frequency Distribution: The data has a high range of values and must be divided into various classes.
Class limits: Smallest and the largest data values of a class.
Class Boundaries: The values used to separate classes to ensure no gap in the frequency distribution.
Class Width: The value obtained by subtracting the lower class limit of one class with the lower class limit of the previous class.
A frequency distribution is the organization of raw data in table form, using classes and frequencies.While drawing an Ogive, we have to put Cumulative frequencies on y-axis and class boundaries on x-axis.
In architecture an ogive is an arch with a pointed apex. It is formed by the intersection of two S curves usually confined to decoration. An ogive or ogival arch is a pointed, "Gothic" arch, drawn with compasses or with arcs of an ellipse
In ballistics and aerodynamics, an ogive is a pointed, curved surface used to form the approximately streamlined nose of a bullet, shell, missile or aircraft.The ogive nose cone is probably one of the most common shapes used in rocketry. It exhibits very good drag characteristics.An example showing plotting of Cumulative Frequency Ogive
A survey was conducted amongst 20 cigarette smokers. The data obtained is given in the chart below. The number of cigarettes smoked by a person, is given in the chart. Construct a frequency distribution using six classes and then draw an Ogive.
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Table
Steps to solve the above problem :
Find the highest and lowest values: H = 22 and L = 5.
Find the range: R = H L = 22 5 = 17.
Given, the number of classes should be 6 (in the last line of the problem statement)
Find the class width by dividing the range by the number of classes. Width = 17/6 = 2.83. This value is rounded up to 3.
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Select a starting point for the lowest class limit. For convenience, this value is chosen to be 5, the smallest data value. The lower class limits will be 5, 8, 11, 14, 17 and 20.
The upper class limits will be 7, 10, 13, 16, 19 and 22. For example, the upper limit for the first class is computed as 8 - 10, etc.Find the class boundaries by subtracting 0.5 from each lower class limit and adding 0.5 to the upper class limit.
Tally the data, write the numerical values for the tallies in the frequency column and find the cumulative frequencies.
Table
Graph
Ogive Plot Curve:
Draw and label the x (horizontal) and the y (vertical) axes.
Represent the cumulative frequencies on the y axis and the class boundaries on the x axis.
Plot the cumulative frequency at each upper class boundary with the height being the corresponding cumulative frequency.
Connect the points with segments. Connect the first point on the left with the x axis at the level of the lowest lower class boundary.
ii.) Since the scale on x- axis starts at 120.5, a kink is shown near the origin on x-axis to indicate that the graph is drawn to scale
beginning at 120.5.
iii. )Take 1 cm along x-axis = 10 cm (height).
iv. )Take 1 cm along y-axis = 20 (pupils)
v. ) Plot the points representing upper class limits and respective cumulative frequencies.
Also plot the point representing lower limit of first class i.e. 120.5-130.5.
vi.) Join these points by a free hand drawing.
The required ogive is hown in the following figure.
