Let us start understanding another significant concept of arithmetic chapter, ‘Averages’ which is an important part of MBA entrance. Although, you might not get direct questions from this chapter in the CAT, MAT, CMAT, XAT and other entrances, but the application of this concept holds strategic importance in enhancing your percentile.
This concept not only helps you in escalating your scores in the Quantitative Aptitude Section, but would also increase your scores in the Data Interpretation section.
Gain a basic understanding of formulas of ‘Averages’ to solve all the questions pertaining to this chapter.
The term Average refers to the sum of all observations divided by the total number of observations. Average is used quite regular in our day to day life. For example to calculate the average marks of the students, Average height of a particular group etc. The term average is also referred to as ‘Mean’. Basic formula to calculate the average is as follows:
Weighted average is calculated with the following formula:
Where, w is the number of occurrences of quantity x.
Arithmetic Mean (AM)
The average of all the terms in an Arithmetic Progression is called its Arithmetic Mean.
Arithmetic mean of the first ‘n’ terms in an A.P. is given by:
Where 'A' is the average of the first and the last terms of the Arithmetic Progression (AP)
Arithmetic Mean can also be obtained by considering any two terms equidistant from both the ends of the AP and taking their average. Hence, the average of the first and the last term will be the same as the average of the second and the second-last term.
Geometric Mean (GM) 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?
It is used when one of the values 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?
Relationship between AM, GM and HM
If AM, GM and HM be the arithmetic, geometric and harmonic means between a and b, then the following results holds:
which is positive if a and b are positive; therefore, the AM of any two positive quantities is greater than their GM.
Also, from equation (iv) we have, GM2 = AMHM
Clearly then, GM is a value that would fall between AM and HM and from equation (v) it is known that AM > GM, therefore we can conclude that GM > HM.
Read Also: Application Based Questions on Averages
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 occur 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.
With the help of given below formulae, we can quickly calculate averages:
Read Also: Problems based on Averages
We hope that these concepts along with their related exercises will aid you in your preparation of Averages chapter.
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