Finding the mean from a table
When data is presented as a list, as in the example below, to find the mean you add up the number of pets owned and divide that by the total number of people asked.
As it would be very easy to make a mistake adding together 50 values we must use a different approach when given the information in a table.
Find the mean number of pets owned.
1. Create a new column ‘Total number of pets’ and calculate the total number of pets in each group by multiplying the number of pets owned by the frequency.
2. Added together gives a total number of 94 pets.
3. Divide the total number of pets by the total of the frequency column to find the mean:
Mean = 94 ÷ 50 = 1.88
Grouped Data
When the data has been grouped we no longer know the exact value of each piece of data.
Instead we calculate the mid-point of the group and take this as the value to represent the whole group.
To calculate the mid-point, add the two end points together and divide by 2.
We can then find the mean as before.
Question
Calculate the mean distance thrown in a discus competition.
- Create two additional columns: midpoint and total
- Calculate the midpoint of each group
- Multiply the midpoint by the frequency
- Sum of totals ÷ total frequency
Mean = 990 ÷ 29 = 34.13793103 m
Mean = 34.14 m (to two decimal places)
