From a series of 50 observations an observation of value 45 is dropped but the mean remain same. What was mean of 50 observation

The mean of a series of numbers is calculated by adding all the numbers together and then dividing by the number of numbers.

Step 1: Let's denote the mean of the 50 observations as M.

Step 2: The sum of the 50 observations would then be 50*M (because mean = sum of observations / number of observations).

Step 3: If we drop an observation of value 45, we have 49 observations left.

Step 4: The sum of these 49 observations would be 50*M - 45 (because we subtract the value of the dropped observation from the total sum).

Step 5: According to the problem, the mean remains the same when the observation is dropped. So, the mean of the 49 observations is also M.

Step 6: Therefore, the sum of the 49 observations can also be calculated as 49*M (because mean = sum of observations / number of observations).

Step 7: Now, we can set up the equation 50M - 45 = 49M and solve for M.

Step 8: If you add 45 to both sides of the equation, you get 50M = 49M + 45.

Step 9: If you subtract 49*M from both sides of the equation, you get M = 45.

So, the mean of the 50 observations was 45.