The maen and midean of 100 observation are 50 and 52 respectively. The value of largest obsrevation is100. It was later found that it is 110 not 100. Find true mean and midean

if the mean was 50, then the total was 100*50

Now, the mean is (100*50 + 10)/50 = 50.2

The median is the same, since the place of the middle value has not changed. This must be so, since it is less than 100, and only the greatest value has changed.

Mean=Sum of observations/total no: of observations

here 50 is the mean
therefore sum of the observation=50*100
so the sum will be 5000

when the value is changed from 100 to 110....only 10 is increased...

therefore sum of observations will be increased by ten....

5000+10(note:100-110)=5010

Mean=Number of Observations/total number of observations

So the mean=5010/100=50.1

i have a small doubt in this problem.....anybody please say my answer is correct or not....if it is wrong please suggest the right way

To find the true mean and median after discovering the mistake in the largest observation, we can follow these steps:

1. Find the sum of all the observations: Since the mean is given as 50 for 100 observations, the sum of all the observations would be 100 * 50 = 5000.

2. Calculate the corrected sum of all observations: Since the largest observation was originally given as 100 but is now corrected to 110, we need to subtract the original value of 100 and add the corrected value of 110. Therefore, the corrected sum of all observations would be 5000 - 100 + 110 = 5010.

3. Find the true mean: The true mean can be calculated by dividing the corrected sum of all observations (5010) by the total number of observations. Therefore, the true mean would be 5010 / 100 = 50.1.

4. Find the true median: The median is the middle value of the ordered set of observations. Since the median is given as 52 for the original set of observations, we need to adjust for the change in the largest observation. The new largest observation is 110, so the true median would still be 52, as the observations below and above the median would remain the same.

Therefore, the true mean is 50.1 and the true median is 52.