Average can be defined as a single value that is meant to typify a data set. It gives a measure of the middle or expected valu e of the data set. Though there are many measures of central tendency, average typically refers to the arithmetic mean and is defined as the ratio of sum of items to the number of items in a dataset.
For example, let’s take heights of the students in a class. If the number of students is 5 and their heights are 168, 170, 169, 174 and 166, then average can be calculated using the above formula as
Average = (168 + 170 + 169 + 174 + 166)/5 = 169.4
Deviation method can always be used instead of using the normal approach towards solving problem. It is much faster and precise as it removes large numbers from the equations and looks at only the smaller deviations from the assumed mean. For example, the average of 71, 72, 73, 74, 75 and 76 can be found by assuming the average of all the numbers to be 73.
The total of all the values of 2nd column is +3. Therefore the average will be 73 + (3/6) = 73.5
Change in Averages
If the values of all the elements in a group are increased or decreased by a same value, the average of the group will also increase or decrease by the same value. If the values of all the elements in a group are multiplied or divided by a same value, the average of the group will also get multiplied or divided by the same value.
An average that looks at the proportional relevance of each component, rather than treating each component equally is called a weighted average. A weighted average with all weights equal will turn into a simple average. A weighted average is always between the smallest and the largest values of the dataset. For example, if the average height of group A is say 180 cm and the average height of group B is say 170 cm, the average of the set comprising of both the groups cannot be determined. It actually depends on the number of people in both the groups. Let’s assume that there are 20 people in group A and 40 people in group B. So, the weighted average = ([20 x 180] + [40 x 170])/60 = 173.33