In the following figures calculate the index number for 2011, on the basis of 2008:
Year: 2008, 2009, 2010, 2011, 2012
Price: 20, 44, 36, 60, 70

Question

In the following figures calculate the index number for 2011, on the basis of 2008: 
Year: 2008, 2009, 2010, 2011, 2012 
Price: 20, 44, 36, 60, 70

Accepted Answer

The correct option is 4:

The problem asks us to calculate a simple price index number for the year 2011, using 2008 as the base year. The calculation of a price index number is a fundamental concept in statistics and economics, used to measure the relative change in price over time. The formula for a simple price index (I) is:
$I = (\text{Price in Current Year } (P\_n) / \text{Price in Base Year } (P\_0)) \times 100$

From the given data:
Base Year $(P\_0)$ is 2008, with Price $= 20$.
Current Year $(P\_n)$ is 2011, with Price $= 60$.

Substituting these values into the formula:
$I\_{2011} = (60 / 20) \times 100$
$I\_{2011} = 3 \times 100$
$I\_{2011} = 300$
This result indicates that the price in 2011 is 300% of the price in 2008, or that there has been a 200% increase in price from the base year. Thus, the index number is 300, confirming Option 4 as correct.

The incorrect option is 1 (150): This result would be obtained if the current price were 30, not 60, or if an incorrect calculation was performed, perhaps by only dividing $P_n$ by 2 without multiplying by 100.

The incorrect option is 2 (600): This value might be obtained by mistakenly multiplying the index number by two, or by calculating the index for a year with a price of 120, which is not provided in the data.

The incorrect option is 3 (120): This result would be incorrect because it suggests only a 20% price increase (since 120 = 100 + 20), which would mean the price in 2011 was 24, not 60.