Question 13 Marks
Average daily wages of 50 workers of a factory was Rs.200. Each worker is given a raise of Rs.20. What is the new average daily wages? Which property of arithmetic mean does the above example point to?
Answer
View full question & answer→Increase in wages of each worker $=$ Rs. 20
Total increase in wages $=50 \times 20=$ Rs. 1000
Total wages before increase in wages $=50 \times 200=$ Rs. 10,000
Total wages after increase in wages $=10,000+1000=$ Rs. 11,000
New average wage $=\frac{\Sigma X}{n}=\frac{11,000}{50}=R s .220$
Thus, the mean wage has increased by Rs. 20 .
The property of arithmetic mean which is reflected here is that if each observation of a series is increased or decreased by a constant, say k, then the arithmetic mean of the new series also gets increased or decreased by k. In this case, each item is increased by 20 , so the mean also increases by 20 .
Total increase in wages $=50 \times 20=$ Rs. 1000
Total wages before increase in wages $=50 \times 200=$ Rs. 10,000
Total wages after increase in wages $=10,000+1000=$ Rs. 11,000
New average wage $=\frac{\Sigma X}{n}=\frac{11,000}{50}=R s .220$
Thus, the mean wage has increased by Rs. 20 .
The property of arithmetic mean which is reflected here is that if each observation of a series is increased or decreased by a constant, say k, then the arithmetic mean of the new series also gets increased or decreased by k. In this case, each item is increased by 20 , so the mean also increases by 20 .
