The following table gives the frequency distribution of trees planted by different Housing Societies in a particular locality:
| No. of Trees | No. of Housing Societies |
| 10-15 | 2 |
| 15-20 | 7 |
| 20-25 | 9 |
| 25-30 | 8 |
| 30-35 | 6 |
| 35-40 | 4 |
Find the mean number of trees planted by Housing Societies by using ‘Assumed Means Method’
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Solution
By Assumed Mean Method
| No. of trees |
Class mark xi |
di=xi-A | No of housing societies(fi) |
fidi |
| 10-15 | 12.5 | -10 | 2 | -20 |
| 15-20 | 17.5 | -5 | 7 | -35 |
| 20-25 |
`22.5toA` |
0 | 9 | 0 |
| 25-30 | 27.5 | 5 | 8 | 40 |
| 30-35 | 32.5 | 10 | 6 | 60 |
| 35-40 | 37.5 | 15 | 4 | 60 |
| Total | - | - |
` sumf_i=36` |
`sumf_id_i=105` |
`bar d=(sumf_id_i)/(sumf_i)=105/36=2.916`
Mean = `bar x=A+bard` = 22.5 + 2.916 = 25.42
Therefore the mean number of trees planted by Housing Societies is 25.42.
Concept: Mean of Grouped Data
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