A price index is calculated for a basket of around 50 items, not all equally weighted. Over a period of time, 75% of items by weight increase in price by amounts that range between 5% and 10% and the price of the remaining 25% fall by amounts ranging between 0% and 5%.Question 22Using the same weightings as before, which one of the following statements about the change in the price index is a valid conclusion?The index will rise by at least 2.5%The index may fallThe index will rise by exactly 5%The index will rise by less than 7%
Question
A price index is calculated for a basket of around 50 items, not all equally weighted. Over a period of time, 75% of items by weight increase in price by amounts that range between 5% and 10% and the price of the remaining 25% fall by amounts ranging between 0% and 5%.Question 22Using the same weightings as before, which one of the following statements about the change in the price index is a valid conclusion?The index will rise by at least 2.5%The index may fallThe index will rise by exactly 5%The index will rise by less than 7%
Solution
The valid conclusion about the change in the price index is that "The index will rise by at least 2.5%".
Here's why:
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75% of the items increased in price by amounts ranging from 5% to 10%. Even if we take the minimum increase of 5%, the overall increase due to these items will be 0.75 * 5% = 3.75%.
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The remaining 25% of the items fell in price by amounts ranging from 0% to 5%. Even if we take the maximum decrease of 5%, the overall decrease due to these items will be 0.25 * 5% = 1.25%.
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If we subtract the overall decrease from the overall increase, we get 3.75% - 1.25% = 2.5%.
So, even in the worst-case scenario (where the price increase for the 75% of items is at the minimum and the price decrease for the 25% of items is at the maximum), the price index will still rise by at least 2.5%. Therefore, the statement "The index will rise by at least 2.5%" is a valid conclusion.
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