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When data is given along with their frequencies. Following is an example of discrete series −
| Items | 5 | 10 | 20 | 30 | 40 | 50 | 60 | 70 |
|---|---|---|---|---|---|---|---|---|
| Frequency | 2 | 5 | 1 | 3 | 12 | 0 | 5 | 7 |
For discrete series, the Arithmetic Mean can be calculated using the following formula.
Formula
$bar{x} = frac{f_1x_1 + f_2x_2 + f_3x_3……..+ f_nx_n}{N}$
Alternatively, we can write same formula as follows −
$bar{x} = frac{sum fx}{sum f}$
Where −
-
${N}$ = Number of observations
-
${f_1,f_2,f_3,…,f_n}$ = Different values of frequency f.
-
${x_1,x_2,x_3,…,x_n}$ = Different values of variable x.
Example
Problem Statement −
Calculate Arithmetic Mean for the following discrete data −
| Items | 14 | 36 | 45 | 70 |
|---|---|---|---|---|
| Frequency | 2 | 5 | 1 | 3 |
Solution −
Based on the given data, we have −
| Items | Frequency f |
${fx}$ |
|---|---|---|
| 14 | 2 | 28 |
| 36 | 5 | 180 |
| 45 | 1 | 45 |
| 70 | 3 | 210 |
| ${N=11}$ | ${sum fx=463}$ |
Based on the above mentioned formula, Arithmetic Mean $bar{x}$ will be −
$bar{x} = frac{463}{11} \[7pt]
, = {42.09}$
The Arithmetic Mean of the given numbers is 42.09.
Calculator
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