Question

Mean of 100 numbers was found to be 50. But later on, it was observed that one of the number 150 was wrongly taken as 50. The correct mean is
49
50
51
52​

Answer 1

Given:

Mean of 100 numbers = 50

One of the number 150 was wrongly taken as 50

To find:

The correct mean of the data

Calculation:

We know the formula

Mean = Sum of numbers / Number of observations      

=> 50 = sum of numbers / 100

=> Sum of observations = 5000

150 is wrongly taken as 50. So the sum of new numbers is

Sum of new numbers = 5000+150-50

                                    = 5100

Correct  mean = Sum of numbers / Number of observations

                        = 5100/100

                        = 51

The correct mean of the data is 51

Answer 2

Answer:

The correct mean is 51.

Step-by-step explanation:

Given data - The mean of 100 numbers is 50. But the fault is that the actual number 150 is substituted by the wrong number 50. Hence, the right mean will be calculated by replacing 50 (wrong value) with 150 (right value).

According to the wrong calculation, the mean of 100 numbers is 50.

(x1+x2+......+x99+50)/100 = 50

x1+x2+......+x99+50 = 5000

x1+x2+......+x99 = 4950 (Equation 1)

The sum of the first 99 numbers is 4950

The correct calculation -

(x1+x2+......+x99+150)/100 = y (Equation 2)

Put the Equation 1 in Equation 2.

(4950+150)/100 = y

y = 51

y (mean) is 51

The correct mean of 100 numbers is 51.

#SPJ6