Averages from Tables

Averages from Tables & Charts

Averages from tables & charts

What are frequency tables?

• Frequency tables are used to summarise data in a neat format

  • They also put the data in order

• For example, the table below shows the number of pets in different houses along a street

  • The number of pets is the data value, x

  • The number of houses is the frequency, f

    • The frequency is how many times a data value is recorded (or seen)

• The total frequency, n, can be calculated by adding together all the values in the frequency column

How do I find the mode from a frequency table?

• The mode is the data value with the highest frequency

  •  The mode for the example above is 1 pet per house

    • The mode is not the frequency, 7, this is the number of houses that have exactly 1 pet

How do I find the median from a frequency table?

• The median is the data value in the middle of the frequency

  • It is the ${\left(\frac{n+1}{2}\right)}^{th}$ value, where $n$ is the total frequency

• From above, $n=20$ so the median is the ${\left(\frac{20+1}{2}\right)}^{th}$ = 10.5^th  value in the table which is the mean of the 10^th and 11^th values

  • The first two rows have a combined (cumulative) frequency of 2 + 7 = 9

  • The first three rows have a combined frequency of 2 + 7 + 6 = 15

  • Therefore the 10th and 11th values are in the third row (x = 2)

    • The median is 2 pets per house

How do I find the mean from a frequency table?

• The mean from a frequency table has the following formula:

  • $\mathrm{mean} =\frac{ \mathrm{total} \mathrm{of} \text{'}\mathrm{data} \mathrm{value} \times \mathrm{frequency}\text{'}}{\mathrm{total} \mathrm{frequency}}$

    • It helps to create a new column of 'data value × frequency'

    • Add up the values in this column

    • Divide by the total frequency

• The mean is $\frac{35}{20}$ = 1.75 pets per house

  • Means do not need to be whole numbers

How do I find the range from frequency tables?

• The range is the difference between the largest and smallest data values

  • The range above is 4 - 0 = 4

    • The range is not the difference between the largest and smallest frequencies

What else should I know about frequency tables?

• Tables can be converted back into a list of data values using their frequencies 

  • From above, 0 pets were recorded twice, 1 pet was recorded 7 times, 2 pets were recorded 6 times, etc

    • The list of pets recorded is 0,0,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,4

• You could then find the mode, median and mean from this list of numbers