How to Find the Midpoint in a Grouped Frequency Distribution

A grouped frequency distribution is a table of the values on some continuous variable, divided into groups. For example, if you were collecting data on income, you might ask people whether their income was under $20,000, $20,000 to $39,999, $40,000 to $59,999, $60,000 to $99,999 or $100,000 or more.

The midpoint, or median, of a continuous variable is the point where half the data are above and half are below.

Instructions

1. Find the total number of respondents. For example, suppose the results of your survey about income are:

   Under $20,000 - 5 people

   $20,000 to $39,999 - 10 people

   $40,000 to $59,999 - 15 people

   $60,000 to $99,999 - 11 people

   $100,000 or more - 9 people

   The total number of people is 5 + 10 + 15 + 11 + 9 = 50.

2. Divide that number in half. In the example, 50/2 = 25. If the number in Step 1 is odd, you can round it down (it will make little difference).

3. Add the number of people in each category until you exceed the number in Step 2. In the example, 5 people are in the lowest category, 5 + 10 = 15 people are in one of the lowest two categories and 5 + 10 + 15 = 30 people are in one of the lowest three categories. Thirty is more than 25, so stop here.

4. Subtract the number in Step 2 from the final sum in Step 3. In the example, 30-25 = 5.

5. Divide the number in Step 4 by the number of people in the highest category included in Step 3. In the example, 5/15 = 0.333.

6. Subtract the lower limit from the upper limit in the highest category in Step 3. In the example, $59,999 - $40,000 = $19,999.

7. Multiply the result in Step 5 by the result in Step 6. In the example, 0.333*$19,999 = $6,659.67.

8. Add the result in Step 7 to the lower limit of the highest category in Step 3. This is the midpoint. In the example, $40,000 + $6,659.67 = $46,659.67.

Tips & Warnings

• This method assumes that the distribution within the middle category is uniform. This is usually a pretty safe assumption.