Question

The table below shows car prices and house prices for the years 2011 and 2012 . Calculate the absolute change and the percentage change in the prices of cars and houses between the years 2011 and 2012 . $$ \begin{array}{|l|l|l|} \hline & 2011 & 2012 \\ \hline \text { Car prices ( } £) & 10000 & 9600 \\ \hline \text { House prices }(£) & £ 200000 & £ 192000 \\ \hline \end{array} $$

Short answer

Car prices decreased by £400 (4%), house prices decreased by £8000 (4%).

Step-by-step solution

Understanding the Data

We are given data in a table showing the prices of cars and houses for the years 2011 and 2012. Our goal is to calculate the absolute change and percentage change for both car prices and house prices between these two years.

Calculate Absolute Change (Car Prices)

The formula for absolute change is: \[ \text{Absolute Change} = \text{Price in 2012} - \text{Price in 2011} \]. For car prices: \[ 9600 - 10000 = -400 \]. The car prices decreased by \( £400 \).

Calculate Absolute Change (House Prices)

Using the same formula for house prices: \[ 192000 - 200000 = -8000 \]. The house prices decreased by \( £8000 \).

Calculate Percentage Change (Car Prices)

The formula for percentage change is: \[ \text{Percentage Change} = \left( \frac{\text{Absolute Change}}{\text{Price in 2011}} \right) \times 100 \]. For car prices: \[ \left( \frac{-400}{10000} \right) \times 100 = -4\% \]. Car prices decreased by 4%.

Calculate Percentage Change (House Prices)

Applying the percentage change formula to house prices: \[ \left( \frac{-8000}{200000} \right) \times 100 = -4\% \]. House prices decreased by 4%.

Key concepts

Absolute Change

When we discuss absolute change, we talk about the exact difference in value between two points in time. It tells us how much more or less one value is compared to another. For the exercise given, absolute change is calculated in monetary units (like pounds in this case). This makes it straightforward to observe how the prices have physically changed.To calculate the absolute change, we use the formula:\[\text{Absolute Change} = \text{Price in 2012} - \text{Price in 2011}\]In the exercise, we calculated the absolute change of car prices as follows:- **Car Prices:** From £10,000 in 2011 to £9,600 in 2012, the absolute change is: \[9600 - 10000 = -400\] indicating that car prices decreased by £400.Similarly, for house prices:- **House Prices:** From £200,000 in 2011 to £192,000 in 2012, the absolute change is: \[192000 - 200000 = -8000\] showing that house prices decreased by £8,000.Absolute change gives us a straightforward number that shows the shift in prices from one year to the next.

Percentage Change

Percentage change provides a way of expressing absolute change as a proportion of the initial value, showing us how significant the change is relative to the original amount. It is useful because it normalizes changes across different scales and allows comparison between various items.The formula for percentage change is given by:\[ \text{Percentage Change} = \left( \frac{\text{Absolute Change}}{\text{Price in 2011}} \right) \times 100 \]Let’s see how this is applied in our exercise:- **Car Prices:** From £10,000 in 2011, dropped to £9,600 in 2012. Applying the formula: \[ \left( \frac{-400}{10000} \right) \times 100 = -4\% \] Therefore, car prices decreased by 4%.- **House Prices:** From £200,000 in 2011, fell to £192,000 in 2012. The percentage change calculation is: \[ \left( \frac{-8000}{200000} \right) \times 100 = -4\% \] Here, house prices also saw a decrease of 4%.Percentage change captures the magnitude of change relative to the starting price, providing an intuitive sense of the change's impact.

Price Comparison

Price comparison involves evaluating different prices to understand both changes over time and differences between various items. By comparing both the absolute change and percentage change of prices, one can make informed decisions or analyses about market trends. In this exercise, we compare the car and house prices over two consecutive years, 2011 and 2012. Here’s what the comparisons show: - Both cars and houses experienced an absolute drop in prices: £400 for cars and £8,000 for houses. - Despite the difference in absolute change, both items saw the same percentage decrease, 4%, indicating a consistent relative drop in both markets. Price comparison not only helps one understand how two prices relate but also allows for assessing how impactful changes are across different scales. For decision-making purposes, it’s important to look not just at raw changes but relative changes to fully grasp the significance and trends of price shifts.