## Finding the Mode, Median and Mean From Frequency Tables

Suppose we start from a frequency table of lengths versus frequencies.

 Length Frequency 0-10 2 10-20 16 20-30 46 30-40 35 40-50 7

Finding the Mode

The mode is just the most common length interval, with the highest frequency: 20-30.

To find the median interval we insert an extra column, a cumulative frequency column.

To find the numbers in the cumulative frequency column we find the totals of the frequency column as we go down.

 Length Frequency Cumulative Frequency 0-10 2 2 10-20 16 2+16=18 20-30 46 2+16+46=64 30-40 35 2+16+46+35=99 40-50 7 2+16+46+35+7=106=99

Finding the Median

The median will lie in the length interval in which the cumulative frequency just passes the halfway point:

The total frequency is 106 so the halfway point is 53.

The cumulative frequency just passes this point in the row where the cumulative frequency is 64, so the median class interval is 20-30

Note: It does not matter how the they label the length intervals:     The calculations are the same as long as the distribution is continuous – if the table involves lengths heights etc.

Finding the Mean

We insert two extra columns – the midpoint and midpoint*frequency columns.

 Length Frequency Midpoint Midpoint*Frequency 0-10 2 5 10 10-20 16 15 240 20-30 46 25 1150 30-40 35 35 1225 40-50 7 45 245 Total 106 2870

The Mean is now the Note: It does not matter how the they label the length intervals:     The calculations are the same as long as the distribution is continuous – if the table involves lengths heights etc. 