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# Frequency tables and the median class interval. (working out the median group from a frequency table)

## How To Work Out The Median From A Grouped Frequency Table Video

Finding the median average from a frequency table can first be done by working out the total frequency. Now the median number is the middle value - so you need to halve the total frequency. This number is where the median value occurs at. So go back to your frequency table, and add up the values in the frequency column until you go past this middle value. This is the place where the median average occurs at. Letâ€™s look at a couple of examples of working out the median average from a frequency table.

**Example 1**

The frequency table below shows the scores of a group of student who took a history exam. Calculate the median test score.

The total frequency is 2 + 7 + 5 + 6 + 10 = 30.

So there are 30 pupils who took the history test.

Now halving 30, you get 15, so the median occurs on the 15^{th} person down the frequency table.

Now if you add up the first 4 rows you go past the number 15 when you reach the 80% row (2+7+5+6 = 20).

Therefore, the median test score is 80%.

**Example 2**

The grouped frequency table below shows the times taken for some runners to complete a half marathon. Work out the median class interval.

The total frequency is 15 + 12 + 7 + 11 + 5 = 50

So there are 50 athletes who completed the half marathon.

Now halving 50, you get 25, so the median occurs on the 25^{th} athlete down the frequency table.

Now if you add up the first 2 rows you go past the number 25 when you reach the 90 up to 120 minute group (15 + 12 = 27).

Therefore, the median class interval for the half marathon is 90 up to 120 minutes.

## Comments

The median of three numbers will be the second. For four numbers it is between the second and third. For five numbers it is the third and so on. For an even number of numbers the median lies between the two middle numbers. If there are an odd number of numbers then you divide by two and add one to get to the middle number. I thought it was worth pointing out but otherwise it is a good explanation. Thank you.