Question

The mean and median of 100 observation are 50 52 resp.The value of the largest observation is 100.It was later found it is 110.Find the true mean and median.

Answer 1

Answer:

True mean = 50.1

True median = 52

Step-by-step explanation:

We are given that the mean and median of 100 observation are 50 and 52 respectively.

Also, the value of the largest observation is 100 but it was later found that it is 110.

So, due to this median will remain unaffected because median is not affected by the extreme values in the data.

So, True median = 52

Mean will get affected by this mistake, i.e.;

Original mean of 100 observations = Sum of all values ÷ No. of observations

                                                 50  =  Sum of all values ÷ 100

So, Incorrect total sum of 100 values = 50 * 100 = 5000

Correct sum of values = 5000 - 100 + 110 = 5010

Correct no. of observations = 100 - 1 + 1 = 100

Therefore, True mean = Correct sum of values ÷ Correct no. of observations

                                     = 5010 ÷ 100 = 50.1