What is the cumulative frequency distribution? We find the cumulative frequency distribution for a class by adding the frequency of that class to the frequencies of all previous classes.

Frequency table

Look at the table above which shows the income of the rich.

The third grade is 29-38. These are people with an income of at least 29 million and at most 38 million.

The frequency of this class is 7. This means that the income of 7 people is at least 29 million and at most 38 million.

What if you wanted to know how many people have incomes of 38 million or less?

You are looking for the cumulative frequency of 29-38 in this case.

Those who have an income of 38 million or less are those whose incomes are 9 million or more and 38 million or less.

Then all you have to do is add 12, 9 and 7

The cumulative distribution of 29-38 equals 12 + 9 + 7 or 28.

The following table shows the cumulative frequency distribution for all classes.

You can also use this formula to calculate the cumulative relative frequency.

Cumulative relative frequency =

Cumulative frequency
/.
Sum of all frequencies

Remember that the sum of all frequencies is 50. For example, the cumulative relative frequency is 39-48 = 36/50 = 0.72

Here is the cumulative frequency distribution table

Cumulative frequency distribution

Indicates a cumulative frequency distribution

A ogive is a line graph showing the cumulative frequencies of the classes.

To graph an ogiv, put that Class boundaries along the x-axis.

To find the class limit of a class, look for the number between the upper limit of that class and the lower limit of the next class.

For example, what are the class limits of 29-38?

To find the lower limit, look for the number between 28 and 29

The number between 28 and 29 is 28.5, so the lower limit is 28.5

To find the upper bound, look for the number between 38 and 39

The number between 38 and 39 is 38.5, so the upper limit is 38.5

  • Note, however, that the lower bound of the first grade is 8.5 (if there was a class before 9-18, the upper bound would be 8. The midpoint between 8 and 9 is 8.5).
  • Also notice that the upper bound of the last class is 68.5 (If there was a class after 59-68, the lower bound would be 69. The midpoint between 68 and 69 is 68.5).

Hence the limits are 8.5, 18.5, 28.5, 38.5, 48.5, 58.5, and 68.5

To graph an ogiv, place all class boundaries on the x-axis.

Make a point above that Upper, higher Limit of each class. The height of the point corresponds to the cumulative frequency of that class.

For example, the upper limit of 39-48 is 48.5 and the cumulative frequency of 39-48 is 36. Make a point above 48.5 that is 36 high.

Connect all points with a straight line.

The ogiv is shown below for the cumulative frequency above.

Ogive for a cumulative frequency distribution

Using the Ogiv to approximate the cumulative frequency of an interval

For example, let’s say you want to find out how many people make 43.5 million or less.

43.5 million are between 38.5 and 48.5.

Just draw a line from the x-axis at 43.5 to the graph. The line intersects the diagram at one point.

From this point, draw a second line from the intersection to the y-axis.

The second line touches the y-axis at 32.

Hence, 32 people can be said to earn 43.5 million or less.


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  1. Cumulative frequency distribution

    May 20, 9 p.m., 4:58 a.m.

    What is the cumulative frequency distribution? We find the cumulative frequency distribution for a class by dividing the frequency of that class …

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