Question

Arithmetic mean of 9 observations is calculated as 38 but in doing so and observation 27 is mistaken for 72 find the actual mean of the data

Answer 1

mean=sum of observations/ total observations
38=sum/9
38×9=sum
342=sum
If a number is mistakenly written as 72 then 45 should be added to the sum
sum=342
actual sum should be :
342+45
=387
mean=sum/total observations
=387/9
= 43

Answer 2

Answer:

33

Step-by-step explanation:

We are given that Arithmetic mean of 9 observations is calculated as 38

Mean = $\frac{\text{sum of all observations}}{\text{No. of observations}}$

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

38*9 = Sum of all observations

342 = Sum of all observations

Now we are given that observation 27 is mistaken for 72

So, new sum of all observations = 342-72+27=297

So, new mean = $\frac{297}{9}$

                        = $33$  

Hence the new mean is 33