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15 எண்களின் சராசரி 25 ஆகவும், அந்த எண்களில் இருந்து 36.2 என்ற ஒரு எண் அகற்றப்பட்டால், மீதமுள்ள எண்களின் சராசரி:
20.8
24.2
21.9
20.1
20.8
Calculate the difference between the removed number and the original mean (36.2 - 25 = 11.2). The new mean will be the old mean minus the deviation (11.2) distributed over the remaining 14 numbers (11.2 / 14 = 0.8). Result = 25 - 0.8 = 24.2.
Total numbers n = 15, Initial mean = 25, Number to remove = 36.2
New Mean=n−1(Initial Mean×n)−Removed Value
Calculate the difference between the removed number and the original mean (36.2 - 25 = 11.2). The new mean will be the old mean minus the deviation (11.2) distributed over the remaining 14 numbers (11.2 / 14 = 0.8). Result = 25 - 0.8 = 24.2.
Students often divide the deviation (11.2) by the original count (15) instead of the remaining count (14).
Calculate total sum of 15 numbers
To find the sum of 15 numbers, multiply the given mean by the count: 15×25=375.
375
Calculate sum of remaining 14 numbers
Subtract the removed number (36.2) from the total sum: 375−36.2=338.8.
338.8
Calculate the new mean
Divide the new sum by the remaining count (14): 338.8/14=24.2.
24.2
B is correct because the calculated mean of the remaining 14 numbers is 24.2.
This concept of 'change in average due to removal/addition' is frequently tested in 'Mixture and Alligation' as well as 'Data Interpretation' sections.
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