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When data is given based on ranges alongwith their frequencies. Following is an example of continous series:
| Items | 0-5 | 5-10 | 10-20 | 20-30 | 30-40 |
|---|---|---|---|---|---|
| Frequency | 2 | 5 | 1 | 3 | 12 |
In case of continous series, a mid point is computed as $frac{lower-limit + upper-limit}{2}$ and Arithmetic Mean is computed using following formula.
Formula
$bar{x} = frac{f_1m_1 + f_2m_2 + f_3m_3……..+ f_nm_n}{N}$
Where −
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${N}$ = Number of observations.
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${f_1,f_2,f_3,…,f_n}$ = Different values of frequency f.
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${m_1,m_2,m_3,…,m_n}$ = Different values of mid points for ranges.
Example
Problem Statement −
Let”s calculate Arithmetic Mean for the following continous data −
| Items | 0-10 | 10-20 | 20-30 | 30-40 |
|---|---|---|---|---|
| Frequency | 2 | 5 | 1 | 3 |
Solution −
Based on the given data, we have −
| Items | Mid-pt m |
Frequency f |
${fm}$ |
|---|---|---|---|
| 0-10 | 5 | 2 | 10 |
| 10-20 | 15 | 5 | 75 |
| 20-30 | 25 | 1 | 25 |
| 30-40 | 35 | 3 | 105 |
| ${N=11}$ | ${sum fm=215}$ |
Based on the above mentioned formula, Arithmetic Mean $bar{x}$ will be −
$bar{x} = frac{215}{11} \[7pt]
, = {19.54}$
The Arithmetic Mean of the given numbers is 19.54.
Calculator
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