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Question
The weekly observations on cost of living index in a certain city for the year 2004 - 2005 are given below. Compute the weekly cost of living index.
| Cost of living Index | Number of Students |
| 1400 - 1500 | 5 |
| 1500 - 1600 | 10 |
| 1600 - 1700 | 20 |
| 1700 - 1800 | 9 |
| 1800 - 1900 | 6 |
| 1900 - 2000 | 2 |
Solution
Let the assume mean A = 1650
| Class interval | Mid valu(x1) |
d1 = x1 - A = x1 - 1650 |
`"u"_1=(x_1-1650)/100` | Frequency(f1) | f1u1 |
| 1400 - 1500 | 1450 | -200 | -2 | 5 | -10 |
| 1500 - 1600 | 1550 | -100 | -1 | 10 | -10 |
| 1600 - 1700 | 1650 | 0 | 0 | 20 | 0 |
| 1700 - 1800 | 1750 | 100 | 1 | 9 | 9 |
| 1800 - 1900 | 1850 | 200 | 2 | 6 | 12 |
| 1900 - 2000 | 1950 | 300 | 3 | 2 | 6 |
| N = 52 | `sumf_1"u"_1=7` |
we have
A = 1650, h = 100
Mean `=A+hxx(sumf_1"u"_1)/N`
`=1650+100xx7/52`
`=1650+700/52`
= 1650 + 13.46
= 1663.46
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