Less Than and Greater Than Cumulative Frequency

Cumulative frequency is a statistical term that represents the total frequency of a value or set of values up to a certain point. It is often used in data analysis and is calculated by adding up all the frequencies of the values before the current value.

Less Than Cumulative Frequency

Less than cumulative frequency is a type of cumulative frequency that represents the total frequency of all the values that are less than or equal to a certain value. It is often used to find the median of a dataset.

For example, consider the following dataset: 1, 2, 3, 4, 5, 5, 6, 7, 8, 9

To calculate the less than cumulative frequency for the value 5, we would add up all the frequencies of the values less than or equal to 5.

Less than cumulative frequency for 5 = frequency of 1 + frequency of 2 + frequency of 3 + frequency of 4 + frequency of 5

= 1 + 1 + 1 + 1 + 2

= 6

Greater Than Cumulative Frequency

Greater than cumulative frequency is a type of cumulative frequency that represents the total frequency of all the values that are greater than or equal to a certain value. It is often used to find the quartiles of a dataset.

Using the same dataset as before, to calculate the greater than cumulative frequency for the value 5, we would add up all the frequencies of the values greater than or equal to 5.

Greater than cumulative frequency for 5 = frequency of 5 + frequency of 6 + frequency of 7 + frequency of 8 + frequency of 9

= 2 + 1 + 1 + 1 + 1

= 6

Differences between Less Than and Greater Than Cumulative Frequency

The key differences between less than and greater than cumulative frequency are:

1. Less than cumulative frequency is used to find the median of a dataset, while greater than cumulative frequency is used to find the quartiles of a dataset.

2. Less than cumulative frequency represents the total frequency of all the values less than or equal to a certain value, while greater than cumulative frequency represents the total frequency of all the values greater than or equal to a certain value.

3. Less than cumulative frequency is calculated by adding up all the frequencies of the values before the current value, while greater than cumulative frequency is calculated by adding up all the frequencies of the values after the current value.

4. Less than cumulative frequency is used to calculate the lower quartile and upper quartile, while greater than cumulative frequency is used to calculate the upper quartile and maximum value.

In conclusion, less than and greater than cumulative frequency are both useful statistical tools for analyzing data. By understanding the differences between them, you can choose the appropriate method to find the statistics that you need.

Less than cumulative frequency distribution:

It is obtained by adding successively the frequencies of all the previous classes including the class against which it is written. The cumulate is started from the lowest to the highest size.

 

More than cumulative frequency distribution:

It is obtained by finding the cumulate total of frequencies starting from the highest to the lowest class.