The Major Shortcuts in Averages

The term average is defined as the ratio taken of the sum of all terms in a given group to the total number of groups. In mathematical terms, the average is also known as Arithmetic Mean or simply the Mean of the numbers.

The mean or average is also used to find the average velocities to have the proper prediction between the vehicles in the race. The shortcut tricks to find the averages are very important in terms of time in the exams.

The formula to find the averages according to the definition can be given as-

Average = (Total Sum of Observations) ÷ (Total Numbers of Observations)

The averages are also used to find the average speeds or velocities, distance, etc.

For a certain family, if we want to find the average age of the family to have a note of the range of the age for that family, this simple method to find the average is used.

Averages are comparatively easy to understand than all other statistical measures. To find the average, one has to be dependent on all the values of a group as the average is found with the help of all the values of the particular group.

The term average has its main term to share the value among all of the given quantities. These shortcut techniques are mostly used in competitive exams to save time.

Some of the examples where the average is found with the help of the shortcut formulae are as shown:

Find the average of the given numbers.

(4,5,6,7,8)

Ans.-> The given numbers are 4,5,6,7,8.

Thus the total number of quantities = 5

Firstly, we have to find the sum of the given numbers, which will be 4+5+6+7+8 = 30

Thus the average will be-

Average = Sum of numbers / Total count of numbers

Average= 30 / 5

Hence,

Average = 6

If we talk in terms of speed, then the formulation can be given from the given information. Suppose, Shweta has covered a distance of X km and the equal distance at Y mph. 

Then the average speed of Shweta during the whole journey can be given as ( 2*X*Y / X+Y).

The questions can also be asked where the average is given and some information about elements is given, and we have to find a particular element of that group. It can be understood with the help of the following example:

The mean or average of five positive integers is 150. If the average of the first two integers is 30 and the average of the fourth and fifth integers is 90. Then find the third number.

Ans.-> As the average of elements is 150 and the total number of elements is 5. Thus, we can calculate the sum of five positive integers as 150 * 5 = 300. 

And we can also find the sum of the first two integers and the sum of the fourth and fifth elements from the given information in a similar way that we found the sum of total numbers as follows:

The sum of the first two numbers = 30 *2 =60 And

The sum of fourth and fifth number = 90 * 2 = 180

Thus, the third number can be found as the difference between the sum of total elements and the sum of the first two numbers, and the fourth and fifth numbers are as follows:

 The third number is = 300 – ( 60+ 180 )

Hence, The third number = 300 – 240 = 60.

Hence, the third number is 60.

Conclusion

Thus, in this article, we have learned about the what are the averages and some short tricks to find the averages. We have also seen the difference between other averages and the arithmetic mean,i.e the simple average, and how they are useful to find the various values and make the predictions or the decisions.