There are three main types of average: mean, mode and median. The mean is what most people mean when they say 'average'. It is found by adding up all of the numbers you have to find the mean of, and dividing by the number of numbers. So the mean of 3, 5, 7, 3 and 5 is 23/5 = 4.6 .
When you are given data which has been grouped, you can't work out the mean exactly because you don't know what the values are exactly (you just know that they are between certain values). However, we calculate an estimate of the mean with the formula: ∑fx / ∑f , where f is the frequency and x is the midpoint of the group (∑ means 'the sum of').
Work out an estimate for the mean height, when the heights of 23 people are given by the first two columns of this table:
Height (cm) Number of People (f) Midpoint (x) fx 101-120 1 110.5 110.5 121-130 3 125.5 376.5 131-140 5 135.5 677.5 141-150 7 145.5 1018.5 151-160 4 155.5 622 161-170 2 165.5 331 171-190 1 180.5 180.5
In this example, the data is grouped. You couldn't find the mean the "normal way" (by adding up the…