A frequency polygon is roughly identical to a histogram used to compare data sets or display a cumulative frequency distribution. It is a visual way of presenting the quantitative data and its frequency.Quantitative data is represented using a line graph.A frequency polygon and a histogram can be used together to get a more accurate view of the distribution shape in some circ*mstances.
When plotting a frequency polygon graph,calculate the midpoint or the classmark for every class interval. The formula for the same is:
Class Mark (Midpoint) = (Upper Limit + Lower Limit) / 2
Statistics focuses on gathering facts and information for a certain reason. For example, In the game of cricket, the statistics of the game are calculated by tabulating each run for each ball. Tables, graphs, pie charts, bar graphs, histograms, polygons, and other graphical representations of statistical data are used.
Read More:Measures of Central Tendency
Table of Content
- Frequency Polygons
- How to Make Frequency Polygons?
- Frequency Polygon Formula
- Advantage of Frequency Polygons
- Difference Between Frequency Polygons and Histogram
- Things to Remember
- Sample Questions
Key Terms: Frequency Polygons, Quantitative Data, Cumulative Frequency Distribution, Statistics, Data Sets
Frequency Polygons
[Click Here for Sample Questions]
Frequency polygons can be defined as agraphical representation of data distribution which helps in understanding the data via the help of a specific shape.
- Frequency polygons are very similar to histograms and help when comparing two or more data.
- The graph helps to show cumulative frequency distribution data by means of a line graph.
- Frequency polygons are expressed in the form of graphs which interprets information used in statistics.
Frequency Polygon
- The visual data form representation help depict the trend and shape of data in an organised and systematic manner.
- Frequency Polygons show the number of occurrences of class intervals via the shape of the graph.
- While a frequency graph is a line graph showing cumulative frequency distribution data, a histogram shows a graph with rectangular bars without spaces.
Terms of Frequency Polygon
Some terms of Frequency Polygon are:
- Class interval-Class interval is a datarange within which the value will fall. This makes the data look easy and basic
- Midpoint- This is the centre point of the bar that will be drawn for the data, and it must be identified for the graph's symmetry.
- Classmark-It is the average of the class interval's upper and lower limits.
- Upper limit-It is the end boundary of the interval.
- Lower limit-It this the first boundary of the interval.
Read Also:
How to Make Frequency Polygons?
[Click Here for Sample Questions]
The following are the steps required to follow for making a frequency polygon:
- Select a class interval and record the results on the horizontal axes.
- Mark the midpoint of every internal at the horizontal axes.
- On vertical axes, mark the frequency.
- Mark a point in the centre of each class interval at the height that corresponds to the frequency of the class interval.
- Join these lines to form a line segment.
- The figure obtained after joining the lines is known as a frequency polygon.
Precaution While Drawing The Curves:
- The points should be shown in a way that they are straight.
- It is necessary to draw rectangles because it shows a wider image of the data that is going to be represented on the graph.
Also Read:
| Chapter-Related Topics | ||
|---|---|---|
| Chi-Square Formula | T-Test Formula | Standard Error Formula |
| Skewness Formula | Median | Coefficient of Variation Formula |
Frequency Polygon Formula
[Click Here for Sample Questions]
When a frequency polygon graph is plotted, the midpoint or the classmark for each of the class intervals is calculated.Thus, theformula for calculating Classmark for each interval is:
Classmark = (Upper limit + Lower limit) / 2
Frequency Polygon Example
An example of a Frequency Polygon can be shown as:
Create a frequency polygon using the following information:
| Test Scores | Frequency |
|---|---|
| 49.5-59.5 | 5 |
| 59.5-69.5 | 10 |
| 69.5-79.5 | 30 |
| 79.5-89.5 | 40 |
| 89.5-99.5 | 15 |
Thus,
Solution- First we need to calculate the cumulative frequency of the given data-
| Test Scores | Frequency | CF |
|---|---|---|
| 49.5-59.5 | 5 | 5 |
| 59.5-69.5 | 10 | 15 |
| 69.5-79.5 | 30 | 45 |
| 79.5-89.5 | 40 | 85 |
| 89.5-99.5 | 15 | 100 |
First, we have to begin plotting the class, such as 54.5, 64.5, 74.5, and so on, all the way up to 94.5. Here,the previous and next class marks to begin and end the polygon, i.e. 44.5 and 104.5.
The frequencies related to each classmark are then plotted against each class mark. Thus, the frequency for class marks 44.5 and 104.5 is zero and touches the x-axis, as shown below. These plot points are simply utilized to give the polygon a closed shape.
This is how the polygon looks:
Test Scores Example
Advantages of Frequency Polygon
[Click Here for Sample Questions]
The advantages of frequency polygon are:
- The frequency polygon not only sorts and represents the data but also makes it easy to make the comparison of the data given.
- Frequency polygons are easy to understand and remember to provide a clear view of the distribution data.
- This method is also less time taking as compared to other methods.
- It's great for comparing two pieces of data that are of the same type especially when the data is vast and continuous.
Types of Frequency Polygon
There are several types of Frequency Polygons, which include:
| Type | Description |
|---|---|
| Frequency Polygon | A frequency polygon is a graph constructed by joining the midpoints of each interval or bin. |
| Absolute Frequency Polygon | Absolute Frequency Polygon has peaks showing the actual number of points in the associated interval. |
| Relative Frequency | It is a histogram graph showing the relative frequency or probability density of a single variable. |
| Relative Frequency Polygon | A Relative Frequency Polygon has peaks showing the percentage of total data points that fall within the interval. |
Difference Between Frequency Polygons and Histogram
[Click Here for Sample Questions]
The difference between Frequency Polygons and Histograms are:
| Frequency Polygon | Histograms |
|---|---|
| A Frequency polygon graph is shown in the form of a curve denoted by a line segment. | A histogram is a graph which shows data via rectangular-shaped bars with no space between them. |
| Here, the midpoint of the frequencies is used. | The frequencies are seen to be spread evenly over the class intervals. |
| The accurate points in a frequency polygon graph demonstrate data of the given class interval. | The data comparison is not visually appealing in a histogram graph. |
Things to Remember
- A frequency polygon is an easy way for grouping the data.
- A frequency polygon graph is a visual way of presenting quantitative data and its frequency.
- A frequency polygon is used to compare data sets or illustrate a cumulative frequency distribution.
- The formula for calculating Classmark for each interval is:Classmark = (Upper limit + Lower limit) / 2
Sample Questions
Ques.What is the difference between a frequency curve and a frequency polygon? (1 mark)
Ans.The difference between a frequency polygon and a frequency curve is that a frequency polygon is drawn by connecting points with a straight line, but a frequency curve is drawn with a free hand. A frequency polygon is very closely similar to a histogram.While, a frequency curve can be obtained by joining the top midpoints of all rectangles of a histogram by means offree hand.
Ques. What is the formula of the Frequency Polygon Graph?(1mark)
Ans. The Formula of the Frequency Polygon Graph is: Class Mark (Midpoint) = (Upper Limit + Lower Limit) / 2.
Ques.Why is a frequency polygon used? (1mark)
Ans.Frequency polygons help us grasp the shape of the data as well as its tendencies.They act likehistograms but are helpful when comparing sets of data. Frequency polygons helpdisplay cumulative frequency distributions.
Ques. What is Relative Frequency Polygon?(1mark)
Ans.A Relative Frequency Polygon can be expressed as a graph with peaks showing the percentage of total data points that fall within the interval.For example, in a test score example, the relative frequency can be calculated by dividing the frequency of a score by the number of scores (N).
Ques. What are the differences between Frequency Polygon and Histogram? (2 marks)
Ans.The differences between Frequency Polygon and Histogram are:
| Frequency Polygon | Histograms |
|---|---|
| A Frequency polygon graph is a form of a curve denoted by a line segment. | A histogram is a graph showing data via rectangular-shaped bars with no space between them. |
| The midpoint, here, of the frequencies is used. | Here, the frequencies spread evenly over the class intervals. |
Ques. What are the uses of frequency polygons? (2 marks)
Ans.Some uses of Frequency Polygons are:
- It is used when the given data is large, and continuous in form.
- It is used while comparing two different sets of data of the same nature.
Ques.Explain the steps involve in constructing a frequency polygon. (3marks)
Ans.For making the polygraph following steps are needed to be followed-
- Make a histogram
- Calculate the midpoint of each bar.
- Placing a point at the beginning and end of the histogram
- Connect the points.
Ques. A frequency distribution's frequency polygon is depicted below.
Answer the following question based on this:
1.What is the average number of students in a class period with a class mark of 15?
2.What is the class interval for a 45th grader?
3.For the distribution, construct a frequency table. (5 marks)
Ans.The following answers can be shown as:
- 18
- 40-50
- The class intervals are 0 – 10, 10 – 20, 20 – 30, 30 – 40, 40 – 50, 50 – 60 since the class marks of consecutive overlapping class intervals are 5, 15, 25, 35, 45, 55. As a result, the frequency table is built as follows.
| Class Interval | Frequency |
|---|---|
| 0 - 10 | 10 |
| 10 - 20 | 18 |
| 20 - 30 | 14 |
| 30 - 40 | 26 |
| 40 - 50 | 8 |
| 50 - 60 | 18 |
Also Check:
