Arithmetic Mean

Arithmetic mean, also called the average or average value, is the quantity obtained by summing two or more numbers or variables and then dividing by the number of numbers or variables. The arithmetic mean is important in statistics.

For example, Let’s say there are only two quantities involved, the arithmetic mean is obtained simply by adding the quantities and dividing by 2.

Some interesting fact about Arithmetic Mean :

- The mean of n numbers x1, x2, . . ., xn is x. If each observation is increased by p, the mean of the new observations is (x + p).
- The mean of n numbers x1, x2, . . ., xn is x. If each observation is decreased by p, the mean of the new observations is (x – p).
- The mean of n numbers x1, x2, . . ., xn is x. If each observation is multiplied by a nonzero number p, the mean of the new observations is px.
- The mean of n numbers x1, x2, . . ., xn is x. If each observation is divided by a nonzero number p, the mean of the new observations is (x/p).

Formula of Arithmetic Mean:

How to find Arithmetic Mean ?

Given three integers A, B and N the task is to find N Arithmetic means between A and B. We basically need to insert N terms in an Arithmetic progression. where A and B are first and last terms.

Examples:

Input : A = 20 B = 32 N = 5 Output : 22 24 26 28 30 The Arithmetic progression series is 20 22 24 26 28 30 32 Input : A = 5 B = 35 N = 5 Output : 10 15 20 25 30

Approach :

Let A1, A2, A3, A4……An be N Arithmetic Means between two given numbers A and B . Then A, A1, A2 ….. An, B will be in Arithmetic Progression. Now B = (N+2)th term of the Arithmetic progression. So :

Finding the (N+2)th term of the Arithmetic progression Series, where d is the Common Difference

B = A + (N + 2 – 1)d B – A = (N + 1)d

So the Common Difference d is given by.

d = (B – A) / (N + 1)

We have the value of A and the value of the common difference(d), now we can find all the N Arithmetic Means between A and B.

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22 24 26 28 30

Time Complexity: O(N)

Auxiliary Space: O(1)

Basic Program related to Arithmetic Mean

- Find Harmonic mean using Arithmetic mean and Geometric mean
- Program for class interval arithmetic mean