Explanation of Class Boundaries and Cumulative Frequencies

Class boundaries are the upper and lower limits of a class interval. They are used to determine the range of values that fall within each class interval. Cumulative frequency, on the other hand, is the sum of the frequencies of all the previous class intervals up to a certain point.

Adding Less Than and More Than Cumulative Frequencies

When we add the less than cumulative frequency and the more than cumulative frequency for a particular class boundary, we get the total frequency for that class interval. This is because the less than cumulative frequency represents the number of observations that fall below the class boundary, while the more than cumulative frequency represents the number of observations that fall above the class boundary.

For example, let's say we have a class boundary of 50. The less than cumulative frequency is 20, and the more than cumulative frequency is 30. This means that there are 20 observations that fall below 50, and 30 observations that fall above 50. Therefore, the total frequency for this class interval is 50 (20 + 30).

Importance of Class Boundaries and Cumulative Frequencies

Class boundaries and cumulative frequencies are important tools in statistics because they allow us to organize data into meaningful intervals and analyze it efficiently. By creating class intervals and calculating cumulative frequencies, we can identify patterns, trends, and outliers in the data. This information can then be used to make informed decisions and predictions.