SAT Math: Finding Statistical Mean or Average
The Math section in Scholastic Aptitude Test, popularly known as SAT exam, comprises at least three to four questions based on average or statistical mean. These questions are amongst the easiest questions in the all the sections devoted to testing the math skills of the SAT students. Therefore, make it a point to attempt these average based questions.
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Finding average is very easy. You probably must be aware of how to find the simple average or mean of a number of values. Using the simple formula,
Average = sum of numbers / total numbers
the total sum of the quantities can be derived by multiplying the total number of quantities with the Average. Similarly the number if quantities is derived by dividing sum of quantities by the average.
Well, this is all that is there to know about formulae for solving SAT average based math problems. However, implementation wise, the questions can be of varied types, as we will presently see.
Example: The average of four girls’ age is 12 years. The ages of three of them are 8, 12 and 13. Find the age of the fourth girl.
Solution: The age of the 4th girl is (4 X 12 ) – (8 + 12 + 13) = 48 – 33 = 7 years.
Solution: The middle number is the fourth number.
Simply subtract the sum of the six numbers from the total sum.
Total sum = 7 X 10.9 = 76.3
Sum of first 3 numbers = 3 X 10.5 = 31.5
Sum of last 3 numbers = 3 X 11.4 = 34.2
Middle number = 76.3 – 65.7 = 10.6
Example: There are three numbers. The second number is half the first number and double the third number. If the average of all the three number is 28, find the numbers.
Solution: Sum of the three numbers = 28 X 3= 84
Let the first number be 4x. The second number would then be 2x and the third would be x.
According to the question, 4x + 2x + x = 7x
7x = 84;
Therefore, x = 12. The three numbers are 48, 24 and 12.
In addition to Average, Arithmetic Progressions are also very frequently asked in the SAT math section. To master the questions based on Arithmetic Progressions, you not only need to remember all the formulae, but also their current use.