Statistics - Arithmetic Mean of Discrete Data Series
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When data is given alongwith 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.
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