[Maths Class Notes] on Ogive Pdf for Exam

The word “Ogive” may be a term utilized in architecture to explain curves or curved shapes. Ogives are graphs that are wont to estimate what percentage numbers lie below or above a specific variable or value in data. To construct an Ogive, firstly, the cumulative frequency of the variables is calculated employing a frequency table. The result or the last number within the cumulative frequency table is usually adequate to the entire frequencies of the variables. The ogives were termed to be intersecting transverse ribs of arches in gothic architecture. They formed the base of the gothic vault. Lancet arch was the pointed, narrow and steep ogive arches.

 

Characteristics

• The ogives are semicircular arches; they are not like the double aux or formats of a cross of ogives.

• The halves of the warheads are ogive branches that mostly radiate around the keystone.

Let us discuss one among the graphs called “Ogive” Here, we are getting to have a glance at what Ogive, graph, chart, and example.

Note: The most commonly used graphs of the distribution are histogram, frequency polygon, frequency curve, Ogives (cumulative frequency curves). 

 

Define Ogive 

The Ogive is defined because of the distribution graph of a series. Ogive is the graph for distribution of the cumulative, which also explains the data values on the horizontal plane axis and either of the cumulative relative frequencies, the cumulative frequencies, or the cumulative percentage frequencies on the vertical axis. Create the Ogive by plotting the purpose like the cumulative frequency of every class interval. Most Statisticians use the Ogive curve, to illustrate the data in the pictorial representation. It helps in estimating the number of observations that are less than or equal to the particular value.

Ogives sometimes are formed the same as the frequency polygons. The essential comparison here is that frequency polygon plot values for themselves whereas the ogives plot values for the cumulative values. To transform a frequency polygon to Ogive we add up the points from left to right in the graph. They are even used to calculate the median, percentiles and the summary of five number data. Here, the median is a basic value that gives us data about the middle of the data given. Thus, considering ogive we get information about the values of data that are above or below a certain allotted median making it feasible to find the median.

Ogive Graph

The graphs of the distribution are frequency graphs that exhibit the characteristics of discrete and continuous data. Such figures are more appealing to the attention than the tabulated data. It helps to facilitate the comparison study for two or more frequency distributions. We can relate the form and pattern of the 2 frequency distributions. The two methods of Ogives are. 

The graph given above represents but and therefore is greater than the Ogive curve. The rising curve is shown (Brown Curve) also represents the Ogive, and therefore the falling curve (Green Curve) represents the greater than Ogive.

 

Less than Ogive

The frequencies of all preceding classes are added to the frequency of a category. This series is known as the less than cumulative series. It is constructed by adding the first-class frequency to the second-class frequency than to the third class frequency than on. The downward cumulation leads to the cumulative series.

Algorithm:

Step1: Find the cumulative frequency distribution by adding class frequencies from the upper limits.

Step2: Now we mark the upper limit on the X-axis at a suitable distance.

Step3: Similarly we mark the cumulative frequencies on the Y-axis at a suitable distance.

Step4: Now we start plotting the upper limit i.e Xn and cumulative frequency i.e Yn on correlation with each other.

Step5: Connect the dots using freehand and form a smooth curve which gives ogive.

Greater than or More than Ogive

The frequencies of the succeeding classes are added to the frequency of a category. This series is named the quiet or greater than cumulative series. It is constructed by subtracting the primary class, second class frequency from the entire, third class frequency from that, and so on. The upward cumulative result is greater than or quite the cumulative series.

Algorithm:

Step1: Find the cumulative frequency distribution by subtracting the class frequency of every class in the order lower towards upper limits from the total frequency.

Step2: Now we mark the lower limit on the X-axis at a suitable distance.

Step3: Similarly we mark the cumulative frequencies on the Y-axis at a suitable distance.

Step4: Now we start plotting the lower limit i.e Xn and cumulative frequency i.e Yn on correlation with each other.

Step5: Connect the dots using freehand and form a smooth curve which gives ogive. 

 

Ogive Chart

An Ogive Chart may be a curve of the cumulative distribution or cumulative frequency distribution. For drawing such a curve, the frequencies must be expressed as a percentage of the entire frequency. Then, such percentages are accumulated and plotted, as within the case of an Ogive. Below are the steps to construct the but and greater than Ogive.

How to Draw Less than an Ogive Curve?

• Draw and mark the horizontal and vertical axes.

• Take the cumulative frequencies along the y-axis (vertical axis) and therefore the upper-class limits on the x-axis (horizontal axis).

• Against each upper-class limit, plot the cumulative frequencies.

• Connect the points with a continuous curve.

How to Draw Greater than or More than the Ogive Curve?

• Draw and mark the horizontal and vertical axes.

• Take the cumulative frequencies along the y-axis (vertical axis) and therefore the lower-class limits on the x-axis (horizontal axis).

• Against each lower-class limit, plot the cumulative frequencies

• Connect the points with a continuous curve.

Uses of Ogive Curve

Ogive Graph or the cumulative frequency graphs are wont to find the median of the given set of knowledge. If both, less than and greater than, the cumulative frequency curve is drawn on the same graph, we can easily find the median value. The point during which, both the curves in
tersect, like the x-axis, gives the median. Apart from finding the medians, Ogives are utilized in computing the percentiles of the info set values.

Creation:

The limits of class intervals for the ogive are marked on the horizontal axis. Referring to the values the points are marked at a height that is the same as the cumulative frequency. To obtain the shape of ogive we connect the points and their adjacent neighbours by a segment. On fewer conditions, the frequency and relative axis might be drawn.

Frequency polygon:

• The curve that helps to find the frequency distribution is known as the frequency curve. The values that are to be hunted for first are the middle values. While plotting the graph we plot the mid values on the x-axis and the frequencies on the y-axis.

• These plotted points are then connected using a line segment. This line is further extended and meets the X-axis. 

• We connect the upper limit to the last point of data and the lower limit to the first point of data. Thus this finally gives us a closed frequency polygon.

Frequency curve: 

The curve that helps to find the frequency distribution is known as the frequency curve. The values that are to be hunted for first are the middle values. While plotting the graph we plot the mid values on the x-axis and the frequencies on the y-axis. These plotted points are connected using a free-hand smooth curve. Thus it is also known as the smoothed freq curve. These points also start and end in the X-axis. The perk of this curve is that the data has a smooth appearance.

Steps to solve an example when a set of data is given:

Step 1: First we need to create a relative frequency table from the data given. And make a tabular form of the heading given below

Class limits

Frequency 

Relative frequency

Step 2: Now we find the cumulative frequency based on the data given above. For finding the cumulative frequency we add up the frequency from right to left.

Class limits

 

Frequency

Relative frequency

Cumulative frequency

Step 3: Now once we have found the cumulative frequency we move ahead and find the relative cumulative frequency.

Class limits 

Relative frequency 

Cumulative frequency

Cumulative frequency relative

Step4: After this, we will plot the x-y graph. The x-axis shows class boundaries whereas they show % cumulative freq on the y axis.

Step 5: Let’s plot the points on the graph now.

While plotting the points the upper limit should be considered first.

Step 6: Join the dots using a line segment. Thus several line segments make up one continuous line which we call ogive. We join these dots from left to right.