If the average wage of 50 workers is Rs 100 and the average wage of 30 of them is Rs 120, then t

step 1 Okay, in this question, we are given the average wages of 50 workers to be 100. Okay, so if we w

If the average wage of 50 workers is Rs 100 and the average...

If the average wage of 50 workers is $\mathrm{Rs} 100$ and the average wage of 30 of them is $\mathrm{Rs} 120$, then the average wage of the remaining workers is
(1) $\mathrm{Rs} 80$
(2) $\mathrm{Rs} 70$
(3) $\mathrm{Rs} 85$
(4) $\operatorname{Rs} 75$

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Key Concepts

Data Partitioning

Data partitioning involves dividing a data set into distinct subgroups, which can then be analyzed separately. When the averages and sizes of some groups are known, this method helps in deducing the missing average or total of the remaining group by using relationships between the parts and the whole.

Arithmetic Mean

The arithmetic mean, or average, is the sum of a set of quantities divided by the number of quantities. It is a measure of central tendency that provides a single value representative of a dataset.

Weighted Average

The weighted average is used when different groups within a dataset contribute unequally. It involves multiplying each subgroup's average by its size, summing these products, and then dividing by the total number of items to find an overall average.

Relationship Between Sum, Count, and Average

This concept highlights that the total sum of values in any dataset is equal to the product of its average and the number of values. It is essential when breaking down a dataset into parts or when some subgroup information is known and the other needs to be determined.

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