Question

Find the arithmetic mean of the progression 2, 4, 6, 8, 10.
A. 10
B. 20
C. 30
D. 6

Answer 1

Hint: Here we use the formula of arithmetic mean of given numbers. Substitute the sum of observations given in the question and divide the sum by the number of observations.
* Arithmetic mean of n numbers is given by dividing the sum of n numbers by ‘n’.

Complete step-by-step answer:
We are given the progression 2, 4, 6, 8, 10
Here the number of observations i.e. terms in the progression is 5
 \[ \Rightarrow n = 5\] … (1)
Now we calculate the sum of given terms of progression.
Let us denote the sum of terms of progression by S
 \[ \Rightarrow S = 2 + 4 + 6 + 8 + 10\]
Calculate the sum of terms in right hand side of the equation
 \[ \Rightarrow S = 30\] … (2)
Now we know that arithmetic mean is given by dividing the sum of observations by the number of observations.
 \[ \Rightarrow \] Arithmetic mean of 2, 4, 6, 8, 10 \[ = \dfrac{S}{n}\]
Substitute the value of sum of observations (S) from equation (2) and number of observation (n) from equation (1)
 \[ \Rightarrow \] Arithmetic mean of 2, 4, 6, 8, 10 \[ = \dfrac{{30}}{5}\]
Now we know we can write \[30 = 6 \times 5\] ; substitute this value of 30 in numerator of the fraction
 \[ \Rightarrow \] Arithmetic mean of 2, 4, 6, 8, 10 \[ = \dfrac{{6 \times 5}}{5}\]
Cancel same factors i.e. 5 from both numerator and denominator of the fraction
 \[ \Rightarrow \] Arithmetic mean of 2, 4, 6, 8, 10 \[ = 6\]
 \[\therefore \] Arithmetic mean of numbers 2, 4, 6, 8 and 10 is 6.

\[\therefore \] Option D is correct.

Note:
Many students make the mistake of leaving the arithmetic mean value in terms of fraction which is wrong, keep in mind we always write the mean value in whole number form or decimal number form.