# Frequency Polygon

19/07/2020A frequency polygon is a graphical form of representation of data. It is used to depict the shape of the data and to depict trends. It is usually drawn with the help of a histogram but can be drawn without it as well. A histogram is a series of rectangular bars with no space between them and is used to represent frequency distributions.

**Steps to Draw a Frequency Polygon**

- Mark the class intervals for each class on the horizontal axis. We will plot the frequency on the vertical axis.
- Calculate the classmark for each class interval. The formula for class mark is:

## Classmark = (Upper limit + Lower limit) / 2

- Mark all the class marks on the horizontal axis. It is also known as the mid-value of every class.
- Corresponding to each class mark, plot the frequency as given to you. The height always depicts the frequency. Make sure that the frequency is plotted against the class mark and not the upper or lower limit of any class.
- Join all the plotted points using a line segment. The curve obtained will be kinked.
- This resulting curve is called the frequency polygon.

Note that the above method is used to draw a frequency polygon without drawing a histogram. You can also draw a histogram first by drawing rectangular bars against the given class intervals. After this, you must join the midpoints of the bars to obtain the frequency polygon. Remember that the bars will have no spaces between them in a histogram.

**Question 1: Construct a frequency polygon using the data given below:**

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 |

**Answer: **We first need to calculate the cumulate frequency from the frequency given.

Test Scores |
Frequency |
Cumulative Frequency |

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 |

We now start by plotting the class marks such as 54.5, 64.5, 74.5 and so on till 94.5. Note that we will also plot the previous and next class marks to start and end the polygon, i.e. we plot 44.5 and 104.5 as well.

Then, the frequencies corresponding to the class marks are plotted against each class mark. Like you can see below, this makes sense as the frequency for class marks 44.5 and 104.5 are zero and touching the x-axis. These plot points are used only to give a closed shape to the polygon. The polygon looks like this: