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Averages from frequency tables

Averages from frequency tables

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Summary

Averages from frequency tables

In a nutshell

Mode, median and mean can all be calculated from frequency tables. If the data being considered is discrete then all of these averages can be calculated, but for any situation where the data is categoric, only the mode can be found.



Calculating averages

​​Mode

​​Procedure

1.
Find the greatest frequency value in the table.
2.
The mode is the data value corresponding to this greatest frequency.


Median

Procedure

1.
Work out the total number of samples taken by summing the frequencies. This value is nn.​
2.
Ensure the rows of the table are written in ascending order for the data value they represent.
3.
The median is the data value that corresponds to the n+12th\dfrac{n+1}{2} th item.​


Mean

​​Procedure

1.
Calculate nn and fill in a third column of the table corresponding to frequency multiplied by the data value.
2.
Calculate the sum of the third column. This value is sum x\text{sum } x.​
3.
The mean is calculated as sum xn\dfrac{\text{sum } x}{n}.


Example 1

Calculate the mode, median and mean from the following frequency table:


Size

Frequency

66
44
6.56.5
77
77
66
88
33


Mode: The most frequent value is 6.5\underline{6.5}


Median: There are 4+7+6+3=204+7+6+3=20 pieces of data. Hence the median occurs at the 20+12=10.5th\dfrac{20+1}{2}=10.5th data item. This is the item between the 10th10th​ piece of data (size 6.56.5​) and the 11th11th​ piece of data (size 6.56.5​). Hence the median is 6.5\underline{6.5}


Mean: Create a third column as follows,


SIZE

FREQUENCY

SIZE x FREQUENCY

66
44
2424
6.56.5
77
45.545.5
77
66
4242
88
33
2424



This third column has a total of 24+45.5+42+24=135.524+45.5+42+24=135.5, and so the mean is:


135.520=6.775\dfrac{135.5}{20}=\underline{6.775}

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Exercises

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FAQs - Frequently Asked Questions

Are frequency tables and frequency distributions the same thing?

When should frequency tables be used?

How do you work out the average from a frequency table?

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