Answer: The resulting mean, after replacing the observation, will be 60.7.
Explanation:
To find the resulting mean after replacing one observation, we need to calculate the new sum of the observations and divide it by the total number of observations.
Given that the original mean of 100 observations is 60, we can calculate the sum of the original 100 observations by multiplying the mean by the total number of observations:
Sum of the original 100 observations = Mean * Total number of observations = 60 * 100 = 6000
To find the new sum after replacing one observation, we subtract the value of the observation to be replaced (50) and add the value of the replacement observation (120):
New sum = Sum of the original 100 observations - Value to be replaced + Value of replacement observation
New sum = 6000 - 50 + 120 = 6070
Since we are still considering 100 observations, we divide the new sum by the total number of observations to find the resulting mean:
Resulting mean = New sum / Total number of observations = 6070 / 100 = 60.7
Therefore, the resulting mean, after replacing the observation, will be 60.7.
I hope this helps :)