Arithmetic Mean
Arithmetic mean is commonly called as average.Mean or Average is defined as the sum of all the given elements divided by the total number of elements.
Formula:
Mean = sum of elements / number of elements
= a1+a2+a3+.....+an/n
Example: To find the mean of 3,5,7.
Step 1: Find the sum of the numbers.
3+5+7 = 15
Step 2: Calculate the total number.
there are 3 numbers.
Step 3: Finding mean.
15/3 = 5
Arithmetic Median
Median is the middle value of the given numbers or distribution in their ascending order.Median is the average value of the two middle elements when the size of the distribution is even.
Example 1: To find the median of 4,5,7,2,1 [ODD].
Step 1: Count the total numbers given.
There are 5 elements or numbers in the distribution.
Step 2: Arrange the numbers in ascending order.
1,2,4,5,7
Step 3: The total elements in the distribution (5) is odd.
The middle position can be calculated using the formula. (n+1)/2
So the middle position is (5+1)/2 = 6/2 = 3
The number at 3rd position is = Median = 4
Example 2: To find the median of 4,5,7,2,1,8 [Even]
Step 1: Count the total numbers given.
There are 6 elements or numbers in the distribution.
Step 2: Arrange the numbers in ascending order.
1,2,4,5,7,8
Step 3: The total elements in the distribution (6) is even.
As the total is even, we have to take average of number at n/2 and (n/2)+1
So the position are n/2= 6/2 = 3 and 4
The number at 3rd and 4th position are 4,5
Step 4: Find the median.
The average is (4+5)/2 = Median = 4.5
Arithmetic Mode
Mode is the most frequently occurring value in a frequency distribution.
Example: To find the mode of 11,3,5,11,7,3,11
Step 1:Arrange the numbers in ascending order.
3,3,5,7,11,11,11
Step 2:
In the above distribution
Number 11 occurs 3 times,
Number 3 occurs 2 times,
Number 5 occurs 1 times,
Number 7 occurs 1 times.
So the number with most occurrances is 11 and is the Mode of this distribution.
Mode = 11
