1. Find index number using Weighted aggregate method
| Item | Quantity | Price0 | Price1 |
| A | 35 | 16 | 18 |
| B | 25 | 40 | 45 |
| C | 20 | 60 | 120 |
| D | 10 | 80 | 90 |
| E | 20 | 30 | 45 |
| F | 15 | 28 | 35 |
Solution:
Weighted aggregate method :
| Item | Weight
`w` | Price
`p_0` | Price
`p_1` | `p_0w` | `p_1w` |
| A | 35 | 16 | 18 | 560 | 630 |
| B | 25 | 40 | 45 | 1000 | 1125 |
| C | 20 | 60 | 120 | 1200 | 2400 |
| D | 10 | 80 | 90 | 800 | 900 |
| E | 20 | 30 | 45 | 600 | 900 |
| F | 15 | 28 | 35 | 420 | 525 |
| --- | --- | --- | --- | --- | --- |
| Total | | | | `sum p_0w=4580` | `sum p_1w=6480` |
Index number by weighted aggregate method
`I=(sum p_1w)/(sum p_0w)xx100`
`=(6480)/(4580)xx100`
`=141.48`
Thus, there is a rise of `(141.48-100)=41.48%` in prices
2. Find index number using Weighted aggregate method
| Item | Quantity | Price0 | Price1 |
| A | 40 | 160 | 200 |
| B | 25 | 400 | 600 |
| C | 5 | 50 | 70 |
| D | 20 | 10 | 18 |
| E | 10 | 2 | 3 |
Solution:
Weighted aggregate method :
| Item | Weight
`w` | Price
`p_0` | Price
`p_1` | `p_0w` | `p_1w` |
| A | 40 | 160 | 200 | 6400 | 8000 |
| B | 25 | 400 | 600 | 10000 | 15000 |
| C | 5 | 50 | 70 | 250 | 350 |
| D | 20 | 10 | 18 | 200 | 360 |
| E | 10 | 2 | 3 | 20 | 30 |
| --- | --- | --- | --- | --- | --- |
| Total | | | | `sum p_0w=16870` | `sum p_1w=23740` |
Index number by weighted aggregate method
`I=(sum p_1w)/(sum p_0w)xx100`
`=(23740)/(16870)xx100`
`=140.72`
Thus, there is a rise of `(140.72-100)=40.72%` in prices
3. Find index number using Weighted aggregate method
| Item | Quantity | Price0 | Price1 |
| A | 40 | 2 | 2.50 |
| B | 20 | 3 | 3.25 |
| C | 10 | 1.5 | 1.75 |
Solution:
Weighted aggregate method :
| Item | Weight
`w` | Price
`p_0` | Price
`p_1` | `p_0w` | `p_1w` |
| A | 40 | 2 | 2.5 | 80 | 100 |
| B | 20 | 3 | 3.25 | 60 | 65 |
| C | 10 | 1.5 | 1.75 | 15 | 17.5 |
| --- | --- | --- | --- | --- | --- |
| Total | | | | `sum p_0w=155` | `sum p_1w=182.5` |
Index number by weighted aggregate method
`I=(sum p_1w)/(sum p_0w)xx100`
`=(182.5)/(155)xx100`
`=117.74`
Thus, there is a rise of `(117.74-100)=17.74%` in prices
This material is intended as a summary. Use your textbook for detail explanation.
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