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If the mean of 20 numbers is 40 and one number 50 is removed, what is the mean of the remaining numbers?
38.5
39.4
37.5
38.9
38.9
Calculate deviation from the mean: the removed number 50 is 50тИТ40=10 above the mean. Distribute this excess loss over the remaining 19 numbers: 40тИТ1910тАЛтЙИ40тИТ0.526=39.47. Note: Check calculation carefully for potential rounding.
Number of observations n = 20, mean of 20 numbers = 40, one number removed = 50
Mean=nтИСxiтАЛтАЛ
Calculate deviation from the mean: the removed number 50 is 50тИТ40=10 above the mean. Distribute this excess loss over the remaining 19 numbers: 40тИТ1910тАЛтЙИ40тИТ0.526=39.47. Note: Check calculation carefully for potential rounding.
Students often divide the new sum by 20 instead of the new count 19 after removing the observation.
Calculate the initial sum
Total sum of 20 numbers is 20├Ч40=800.
Sum20тАЛ=20├Ч40=800
Subtract the removed number
Subtract 50 from the total sum to get the sum of the remaining 19 numbers.
Sum19тАЛ=800тИТ50=750
Calculate the new mean
Divide the new sum 750 by the new count 19.
New┬аMean=19750тАЛтЙИ39.47
B is correct because the calculated mean is approximately 39.47, which rounds to the provided option 39.4.
This concept of 'change in average' is frequently tested in 'Weighted Averages' and 'Alligation' problems in Data Interpretation sections.