CAT Quantitative Aptitude: Basics of Averages

Average is the sum of quantities divided by the number of quantities.

That is if the quantities are x1,x2,x3,x4 and x5, then the average of the 5 quantities is given by

Example: Five persons have 1, 2, 3, 4 and 5 apples with them the average number of apples with each of them is given by

Average is similar to arithmetic mean in calculation.

Weighted average is calculated with the following formula:

Where, w is the number of occurrences of quantity x.

Example: Two pupil in a class score 40, four pupil score 50 and another four 60. What is the average mark of the class?

Geometric mean is to be used when you work with values derived from percentage.

It is calculated as follows:

Example: The returns of an investment of Rs 1000 are 110%, 120% and 130% for three months. What is the mean?

Harmonic mean

It is used when one of the value is unusually lower or higher compared to other values.

Example: The distance between two cities is divided into three parts and a man drives the three parts at speeds of 10 kmph, 40 kmph and 50 kmph respectively. What is the average speed?

Median:

Median of a finite set of numbers is the number in the middle position when arranged in an increasing order.

Example: The salaries (in thousands) of 5 people are 10, 20, 15, 45, 36. What is the median?

In 10, 15, 20, 36, and 45, the median is 20.

If the number of elements is even, then the median is the average of the two middle values.

Mode:

Mode is the element that occurs the maximum number of times in a set.

Example: On 10 fair roll of a dice the following are the results: 1, 2, 5, 4, 1, 3, 6, 3, 2, and 1.

The mode is 1.

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