Definition of Weighted average

The definition of weighted average is
its the average of two or more groups. Weighted average is a number closer to the average of the group that contains more number of terms.
Weighted average or weighted mean is the average of two or more groups.
Consider a cricket team of 11 players.
Divide them into two teams.
One team has 5 bowlers and another team has 6 batsmen.
Let the average age of the bowlers’ team be 20 years and that of the batsmen’ 26.
Now, what will be the average age of all the 11 players Or
What is the weighted mean age of the two teams combinedly?
The following table describes the data:
The Weighted average of the two teams of bowlers and batsmen is 23.3 rounded to the tenth.
weighted average PROPERTY
As a rule, the weighted mean is always closer to the average of the group that contains more number of terms.
This is what weight signifies in the name weighted average.
Weightage is greater weight resulting from greater number of terms.
Whichever group has greater number of terms carries greater weight.
And therefore, the weighted average leans to the average of this group.
In the above example, between the two averages 20 and 26, it is 26 to which the weighted average 23.3 is nearer to, because, 26 is the average age of the batsmen - the group that contains more number of terms.
Solve the following question using the above rule on weighted average:
In an institute having 20 employees of faculty and managers, there are 11 managers whose average salary is P. The average salary of the faculty, which is less than that of the others, is Q.
Is the average salary of all the 20 members in the office greater than
(P + Q)/2?
Answer:
(P + Q)/2 is the mid-point of P and Q.
The number of managers is more than the number of faculty.
Therefore, weighted mean will lie closer to P than to Q.
Also, since P is greater than Q, therefore weighted average lying closer to P will move beyond (P + Q)/2.
Therefore, weighted average is greater than (P + Q)/2 Read, Understand and Rememeber easily Math formulas for school and entrance exams with perfect graphics and simple but succinct descriptions of the pictures at my Pinterest:
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[@math-for-all-gradescom]

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[@gnu3166]

Thanks for simple explanation. The last bit about characteristic of weighted avereage being closer to the larger group was very helpful

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[@joshuaidumijie9129]

Thinking about it... The formula is still same as sum/frequency. So, how does it then differ than the regular mean. When you have a small sample size, the effect of outliers tends to be more pronounced and when you have a larger data, the mean tends to skew towards the mode. I am no Statistician but why call it a new name when it is same as just calculating the combined mean of two groups.

[@ritikaverma4461]

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Superb way explaining the concept of weighted average, Thank you Sir

[@math-for-all-gradescom]

Tq Deepak

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Sir, how the weight of the numbers is determined?

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