Question

arithmetic mean of nine observation is calculated as 38.but in doing so,an observation27 is mistaken for 72. Find the actual mean of data

Answer 1

Mean of 9 observations =38
total sum of 9 observations =9×38=342
since 27 is mistaken as 72
correct sum of 38 observation =342-72+27=297
correct mean=297÷9=33

Answer 2

Answer:

33

Step-by-step explanation:

We are given that arithmetic mean of nine observation is calculated as 38.

$Average = \frac{\text{Sum of all observations}}{\text{total no. of observations}}$

$38 = \frac{\text{Sum of all observations}}{9}$

$38 \times9 =\text{Sum of all observations}$

$342 =\text{Sum of all observations}$

So, Sum of all observations = 342

Now we are given that an observation 27 is mistaken for 72.

So, new sum  =  342-72+27 =297

So,$\text{new Average} = \frac{\text{New Sum}}{\text{total no. of observations}}$

$\text{new Average} = \frac{297}{9}$

$\text{new Average} =33$

Hence the new average is 33