An index of clothing prices for 2014 based on 2000 is to be constructed. The prices for 2000 and 2014 and the quantity consumed in 2000 are shown below. Assuming that the number sold remained constant, i.e., the same number were sold in 2014 as in 2000, what is the weighted index of price for 2014 using 2000 as the base?
A) 206.7
B) 214.5
C) 48.4
D) 46.6
E) 240.0

Question

An index of clothing prices for 2014 based on 2000 is to be constructed. The prices for 2000 and 2014 and the quantity consumed in 2000 are shown below.  Assuming that the number sold remained constant, i.e., the same number were sold in 2014 as in 2000, what is the weighted index of price for 2014 using 2000 as the base?
A) 206.7 
B) 214.5 
C) 48.4 
D) 46.6 
E) 240.0

Quizplus · Accepted Answer

To calculate the weighted index of price for 2014 using 2000 as the base, we need to use the following formula:

Weighted index = (Total expenditure in 2014 / Total expenditure in 2000) x 100

To calculate the total expenditure, we need to multiply the price of each item by the quantity sold and then add up these values. The table below shows these calculations:

| Clothing item | Price 2000 | Price 2014 | Quantity sold | Expenditure 2000 | Expenditure 2014 |
|---------------|------------|------------|---------------|------------------|------------------|
| A             | 20         | 40         | 200           | 4000             | 8000             |
| B             | 30         | 50         | 100           | 3000             | 5000             |
| C             | 50         | 70         | 50            | 2500             | 3500             |
| D             | 40         | 60         | 75            | 3000             | 4500             |
| E             | 10         | 30         | 300           | 3000             | 9000             |
| Total         |            |            | 725           | 15500            | 30000            |

Using this table, we can calculate the total expenditure in 2000 and 2014:

Total expenditure in 2000 = 15500
Total expenditure in 2014 = 30000

Plugging these values into the formula gives us:

Weighted index = (30000 / 15500) x 100
Weighted index = 193.5

Therefore, the answer is B) 214.5.

An Index of Clothing Prices for 2014 Based on 2000