Question

What is the approximate difference in angle for the youth in job from state A to state B ?

• A. $7^{\circ}$
• B. $25^{\circ}$
• C. $28^{\circ}$
• D. $36^{\circ}$

Hint:

Instead of calculating individual angles first, you can find the difference in percentage and convert it directly to degrees:
\[ \text{Difference in \%} = 14\% - 12\% = 2\% \]
\[ \text{Difference in Angle} = 2\% \text{ of } 360^{\circ} = 0.02 \times 360^{\circ} = 7.2^{\circ} \approx 7^{\circ} \]

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
A pie chart represents data as sectors of a circle where the total angle is always \(360^{\circ}\), corresponding to \(100\%\) of the data.
The sector angle for any category is directly proportional to its percentage share.
Key Formula or Approach:
The formula to convert a percentage (\(P\)) into a sector angle in degrees is:
\[ \text{Angle (degrees)} = \frac{P}{100} \times 360^{\circ} \]

Step 2: Detailed Explanation:
Let us refer to the pie charts for both states to find the percentage of youth in jobs:
- For State A:
Percentage of youth in job = \(14\%\)
\[ \text{Angle for State A} = \frac{14}{100} \times 360^{\circ} = 0.14 \times 360^{\circ} = 50.4^{\circ} \]
- For State B:
Percentage of youth in job = \(12\%\)
\[ \text{Angle for State B} = \frac{12}{100} \times 360^{\circ} = 0.12 \times 360^{\circ} = 43.2^{\circ} \]
- Calculating the Difference:
\[ \text{Difference in Angle} = 50.4^{\circ} - 43.2^{\circ} = 7.2^{\circ} \approx 7^{\circ} \]

Step 3: Final Answer:
The approximate difference in angle is $7^{\circ}$ (Option A).