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: Word Problems

Average

Video Lesson: Average

The term average can technically refer to a variety of mathematical ideas, but on the test, it refers to the arithmetic mean. It is found by adding the numbers given and then dividing this sum by the number of items being averaged. Hence the basic equation for average questions is:

Averages Note

Just in simple words, on the Test, the average (also called arithmetic mean) of a set of 5 numbers is simply the sum of all the numbers divided by 5. In other words, if you want to find the average of three numbers add them up and divide by 3.

Average Example 01

Single Unit Quantities

The Test does not always write average questions with clear solutions. The easy questions base normally on single unit quantities like Currency, temperature, height, weight (Kgs). If the question on the Test gives you the monthly incomes (in any currency) of five persons, you can find the average simply by adding the income of all five persons and then dividing it by 5.

Sum of entities = (Number of entities) × Average. The average of two numbers is 5, the sum of the numbers is 5×2 = 10.

Average is also called as mean or arithmetic mean. It gives the central value of data.

Averages (Mixed Unit Quantities)

The quantities described by at least two other quantities cannot be averaged by using the basic equation of arithmetic mean rather, to feel comfortable in time management, you’ll have to use CAT table method explained by following examples.

Some Common Double Unit Entities

Averages Formulae

To Find Average Price

Average Price = Total Value Total Quantity

Example:

A man buys 5 Kg of Mangoes at the price of Rs. 80 per Kg. Next time, he purchases 10 Kg of mangoes at the price of Rs. 90 per Kg. Find the average price per Kg of the two transactions.

Solution:

Use CAT table method for mixed unit quantities.

Averages Cat Table

15 x = 1500, x = 100 (Average price for 15 Kg mangoes)

Average of Averages

First, apply basic equation of average to find the sum of each average given, then add all sums and divide it by sum of all ns (numbers).

Example:

A boy scored 55 in average of five tests. He scored 65 in average of first two tests. What is his average score in last three tests?

Solution

Since, this is the case of double unit entities so apply CAT table method.

Average Of Averages 01

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