If in the starting if there is a big gap b/w class intervals nd then their gap is. Common....... To cover that big jump we've to put the kink

Introduction:

A frequency polygon is a graphical representation of the distribution of a dataset. It is constructed by joining the midpoints of the tops of the bars in a histogram. Each midpoint represents a specific class interval, and its height is determined by the frequency or relative frequency of that interval. The resulting graph displays the shape, center, and spread of the data.

Definition of a Kink:

A kink in a frequency polygon refers to a sudden change in direction or slope of the line connecting the midpoints of the histogram bars. It occurs when there is a significant change in the frequency or relative frequency between adjacent class intervals.

Reasons for a Kink in a Frequency Polygon:

There are several reasons why a kink may occur in a frequency polygon:

1. Discontinuous Data: If the data being represented is discontinuous, such as a categorical variable, it can result in a kink in the frequency polygon. This is because there may be a sudden change in the frequency or relative frequency between adjacent categories.

2. Outliers: Outliers, which are extreme values in the dataset, can also cause a kink in the frequency polygon. If there is a significant outlier that falls outside the range of the other data points, it can result in a sudden change in frequency and create a kink in the graph.

3. Sampling Errors: Sampling errors, which occur when the sample data does not accurately represent the population, can lead to kinks in the frequency polygon. If the sample is not representative, it may result in a sudden change in frequency between adjacent class intervals.

4. Data Manipulation: In some cases, the data may have been manipulated or categorized in a way that introduces kinks in the frequency polygon. This can occur when the data is incorrectly grouped or when there are inconsistencies in the way the data is recorded.

Conclusion:

In summary, a kink in a frequency polygon can occur due to various reasons such as discontinuous data, outliers, sampling errors, or data manipulation. It represents a sudden change in the frequency or relative frequency between adjacent class intervals. Understanding the presence of kinks in a frequency polygon is important for interpreting and analyzing the distribution of the data accurately.