Question

Marks of 12 students in a unit test are given as 4,21,13,17,5,9,10,20,19,12,20,14.assume a mean and calculate the arithmetic mean of the data

Answer 1

arithmetic mean=sum of the observation divided by number of observations
avg=(4+21+13+17+5+9+10+20+19+12+20+14)/12
avg=164/12
mean=13.66

Answer 2

Answer:

Definition : The arithmetic mean is nearest to assumed mean but not equal.

Marks of 12 students in a unit test are given as 4,21,13,17,5,9,10,20,19,12,20,14.

Arrange the data is ascending order

4,5,9,10,12,13,14,17,19,20,20,21

Assumed mean is almost the median of the data.

Median of 12 terms is $M=\frac{6th+7th}{2}$

$Median=\frac{13+14}{2}$

$Median=\frac{27}{2}$

$Median=13.5$

So, assumed mean = 13.5

Now arithmetic mean = Sum of all observations divided by number of observation:

So,$AM =\frac{4+5+9+10+12+13+14+17+19+20+20+21}{12}$

So,$AM =13.66$

Thus the arithmetic mean is nearest to assumed mean