Compute the weighted aggregative index number for the following data:
|
Variable |
Price |
Weights |
|
|
Current year |
Base year |
||
|
X |
5 |
4 |
60 |
|
Y |
3 |
2 |
50 |
|
Z |
2 |
1 |
30 |
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 137.84
The weighted aggregative price index is given by:
$P_{01} = \frac{\sum p_1 W}{\sum p_0 W} \times 100$
Calculation Table:
|
Variable |
$p_1$ (Current) |
$p_0$ (Base) |
W (Weight) |
$p_1W$ |
$p_0W$ |
|
X |
5 |
4 |
60 |
$5 \times 60 = 300$ |
$4 \times 60 = 240$ |
|
Y |
3 |
2 |
50 |
$3 \times 50 = 150$ |
$2 \times 50 = 100$ |
|
Z |
2 |
1 |
30 |
$2 \times 30 = 60$ |
$1 \times 30 = 30$ |
|
Total |
|
|
|
$\sum p_1 W = 510$ |
$\sum p_0 W = 370$ |
Apply the formula:
$P_{01} = \frac{510}{370} \times 100$
$P_{01} \approx 1.378378 \times 100$
$P_{01} = 137.84$