Data Interpretation Solution: PC Production and Sales Analysis

This problem requires us to analyze the provided table which details the number of Personal Computers (PCs) produced and the percentage of PCs sold by two companies, A and B, over several years. We need to use this data to find a specific ratio involving the number of PCs sold and unsold by these companies in particular years.

The table provides the following information:

Calculating PCs Sold by Company B in 2018

First, let's find the number of PCs sold by Company B in the year 2018.

• From the table, the number of PCs produced by Company B in 2018 is 65 thousand.
• The percentage of PCs sold by Company B in 2018 is 80%.

To find the number of PCs sold, we calculate 80% of the total production.

Number of PCs sold by Company B in 2018 $= \text{Production} \times \frac{\text{Percentage Sold}}{100}$

Number of PCs sold by Company B in 2018 $= 65 \text{ thousand} \times \frac{80}{100}$

Number of PCs sold by Company B in 2018 $= 65 \times 0.8 = 52$ thousand PCs.

So, Company B sold 52,000 PCs in 2018.

Calculating PCs Unsold by Company A in 2015

Next, let's find the number of PCs that remained unsold by Company A in the year 2015.

• From the table, the number of PCs produced by Company A in 2015 is 52 thousand.
• The percentage of PCs sold by Company A in 2015 is 75%.

If 75% of PCs were sold, then the percentage of PCs unsold is the remaining percentage out of 100%.

Percentage of PCs unsold by Company A in 2015 $= 100\% - \text{Percentage Sold}$

Percentage of PCs unsold by Company A in 2015 $= 100\% - 75\% = 25\%$

Now, we calculate 25% of the total production by Company A in 2015 to find the number of unsold PCs.

Number of PCs unsold by Company A in 2015 $= \text{Production} \times \frac{\text{Percentage Unsold}}{100}$

Number of PCs unsold by Company A in 2015 $= 52 \text{ thousand} \times \frac{25}{100}$

Number of PCs unsold by Company A in 2015 $= 52 \times 0.25 = 13$ thousand PCs.

So, Company A had 13,000 unsold PCs in 2015.

Calculating the Ratio of Sold PCs (B) to Unsold PCs (A)

The question asks for the ratio of the number of PCs sold by Company B in 2018 to the number of PCs that remained unsold by Company A in 2015.

Ratio $= \frac{\text{Number of PCs sold by Company B in 2018}}{\text{Number of PCs unsold by Company A in 2015}}$

Using the values we calculated:

Ratio $= \frac{52 \text{ thousand}}{13 \text{ thousand}}$

Ratio $= \frac{52}{13}$

Simplifying the fraction by dividing both the numerator and denominator by 13:

Ratio $= \frac{52 \div 13}{13 \div 13} = \frac{4}{1}$

The ratio is 4:1.

Therefore, the ratio of the number of PCs sold by Company B in 2018 to the number of PCs that remained unsold by Company A in the year 2015 is 4:1.

Revision Table: Key Calculations Summary

Ratio of (PCs sold by B in 2018) : (PCs unsold by A in 2015) = 52 : 13 = 4 : 1.

Additional Information: Data Interpretation Basics

Data interpretation questions like this test your ability to extract, calculate, and compare information from tables, charts, or graphs. Here are some key points:

• Understand the Data: Always read the titles, headings, and labels carefully to know what the data represents and the units used (e.g., in thousands).
• Identify the Question: Clearly understand what is being asked. Break down the question into smaller steps if necessary.
• Locate Relevant Data: Find the specific numbers in the table needed for your calculations.
• Perform Calculations: Carry out the arithmetic operations required (addition, subtraction, multiplication, division, percentage calculations, ratios).
• Percentage Calculations: Remember that a percentage is a fraction out of 100. To find a percentage of a number, convert the percentage to a decimal or fraction and multiply. E.g., 80% of 65 is $0.80 \times 65$.
• Unsold vs. Sold: If you have the percentage sold, the percentage unsold is 100% minus the percentage sold.
• Ratios: A ratio is a comparison of two numbers. It can be written as $a:b$ or $a/b$. Ratios should be simplified to their simplest form by dividing both parts by their greatest common divisor.
• Units: Pay attention to units (like "in Thousands") throughout your calculation and in the final answer. In this case, since we were finding a ratio of two numbers in thousands, the "thousands" unit cancels out.

Practicing with different types of data representation (tables, bar graphs, pie charts, line graphs) will help you improve your data interpretation skills.