1. Find index number using Weighted average of price relatives 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 average of price relatives method :
| Item | Weight
`W` | Price
`p_0` | Price
`p_1` | Price relatives
`I=p_1/p_0 xx 100` | `IW` |
| A | 35 | 16 | 18 | `18/16 xx 100=112.5` | 3937.5 |
| B | 25 | 40 | 45 | `45/40 xx 100=112.5` | 2812.5 |
| C | 20 | 60 | 120 | `120/60 xx 100=200` | 4000 |
| D | 10 | 80 | 90 | `90/80 xx 100=112.5` | 1125 |
| E | 20 | 30 | 45 | `45/30 xx 100=150` | 3000 |
| F | 15 | 28 | 35 | `35/28 xx 100=125` | 1875 |
| --- | --- | --- | --- | --- | --- |
| Total | `sum W=125` | | | | `sum IW=16750` |
Index number by weighted average of price relatives method
`I=(sum IW)/(sum W)`
`=(16750)/(125)`
`=134`
Thus, there is a rise of `(134-100)=34%` in prices
2. Find index number using Weighted average of price relatives 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 average of price relatives method :
| Item | Weight
`W` | Price
`p_0` | Price
`p_1` | Price relatives
`I=p_1/p_0 xx 100` | `IW` |
| A | 40 | 160 | 200 | `200/160 xx 100=125` | 5000 |
| B | 25 | 400 | 600 | `600/400 xx 100=150` | 3750 |
| C | 5 | 50 | 70 | `70/50 xx 100=140` | 700 |
| D | 20 | 10 | 18 | `18/10 xx 100=180` | 3600 |
| E | 10 | 2 | 3 | `3/2 xx 100=150` | 1500 |
| --- | --- | --- | --- | --- | --- |
| Total | `sum W=100` | | | | `sum IW=14550` |
Index number by weighted average of price relatives method
`I=(sum IW)/(sum W)`
`=(14550)/(100)`
`=145.5`
Thus, there is a rise of `(145.5-100)=45.5%` in prices
3. Find index number using Weighted average of price relatives method
| Item | Quantity | Price0 | Price1 |
| A | 40 | 2 | 2.50 |
| B | 20 | 3 | 3.25 |
| C | 10 | 1.5 | 1.75 |
Solution:
Weighted average of price relatives method :
| Item | Weight
`W` | Price
`p_0` | Price
`p_1` | Price relatives
`I=p_1/p_0 xx 100` | `IW` |
| A | 40 | 2 | 2.5 | `2.5/2 xx 100=125` | 5000 |
| B | 20 | 3 | 3.25 | `3.25/3 xx 100=108.3333` | 2166.6667 |
| C | 10 | 1.5 | 1.75 | `1.75/1.5 xx 100=116.6667` | 1166.6667 |
| --- | --- | --- | --- | --- | --- |
| Total | `sum W=70` | | | | `sum IW=8333.3333` |
Index number by weighted average of price relatives method
`I=(sum IW)/(sum W)`
`=(8333.3333)/(70)`
`=119.05`
Thus, there is a rise of `(119.05-100)=19.05%` in prices
This material is intended as a summary. Use your textbook for detail explanation.
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