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15 ಸಂಖ್ಯೆಗಳ ಸರಾಸರಿ 25 ಆಗಿದ್ದರೆ ಮತ್ತು ಒಂದು ಸಂಖ್ಯೆ 36.2 ಅನ್ನು ಸಂಖ್ಯೆಗಳಿಂದ ತೆಗೆದುಹಾಕಿದರೆ, ಉಳಿದ ಸಂಖ್ಯೆಗಳ ಸರಾಸರಿ ಹೀಗಿರುತ್ತದೆ:
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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