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. Assume another number as mean calculate the arithmetic mean again.Do you get the same result. Comment.

Answer 1

Arange in asending order
that is 4,5,9,10,12,13,14,17,19,20,20,21.
Assumed mean is either 13 or 14.
Arithmatic mean= 4+5+9+10+12+13+14+17+19+20+20+21=164/12= 13.666
Mean is not same as assumed mean.

Answer 2

Answer:

The arithmetic mean is closest to assumed mean but not equal.

Step-by-step explanation:

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

To find : Assume a mean and calculate the arithmetic mean of the data.

Solution :

Arrange the data from ascending to descending,

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 $M=\frac{6th+7th}{2}$

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

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

$M=13.5$

Arithmetic mean is defined as the sum of observation upon total number of observation.

$A.M=\frac{\sum x_n}{n}$

$A.M=\frac{4+5+9+10+12+13+14+17+19+20+20+21}{12}$

$A.M=\frac{164}{12}$

$A.M=13.6$

Therefore, The arithmetic mean is closest to assumed mean but not equal.