Statistical Representation of DataMCQPYQ Dec 21Question 2768 of 295
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A student makes in five subject S1,S2,S3,S4\displaystyle S1, S2, S3, S4 and S5\displaystyle S5 are 86,79,90,88\displaystyle 86, 79, 90, 88 and 89\displaystyle 89. If we need to draw a Pie chart to represent these markers, then what will be the Central angle for S3\displaystyle S3.

Options

A103.2∘\displaystyle 103.2^{\circ}
B75∘\displaystyle 75^{\circ}
C105.6∘\displaystyle 105.6^{\circ}
D94.8∘\displaystyle 94.8^{\circ}
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Correct Answer

✅ Option b — 75∘\displaystyle 75^{\circ}

All Options:

  • A103.2∘\displaystyle 103.2^{\circ}
  • B75∘\displaystyle 75^{\circ}
  • C105.6∘\displaystyle 105.6^{\circ}
  • D94.8∘\displaystyle 94.8^{\circ}

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Detailed Solution & Explanation

To represent data in a pie chart, each category's value is converted into a sector of the circle. The central angle θ\displaystyle \theta for any component is proportional to its contribution to the total sum of all components:\nθ=Component ValueTotal Value×360∘\theta = \frac{\text{Component Value}}{\text{Total Value}} \times 360^{\circ}\n\n1. **Calculate the Total Marks** across all five subjects (S1,S2,S3,S4,S5\displaystyle S_1, S_2, S_3, S_4, S_5):\n Total Marks=86+79+90+88+89=432\text{Total Marks} = 86 + 79 + 90 + 88 + 89 = 432\n\n2. **Identify the marks for subject S3\displaystyle S_3**:\n Marks in S3=90\text{Marks in } S_3 = 90\n\n3. **Calculate the Central Angle for S3\displaystyle S_3**:\n θS3=90432×360∘\theta_{S3} = \frac{90}{432} \times 360^{\circ}\n - Simplifying 90432\displaystyle \frac{90}{432}:\n 90432=1048=524\frac{90}{432} = \frac{10}{48} = \frac{5}{24}\n - Calculating the angle:\n θS3=524×360∘=5×15∘=75∘\theta_{S3} = \frac{5}{24} \times 360^{\circ} = 5 \times 15^{\circ} = 75^{\circ}\n\nThus, the central angle for S3\displaystyle S_3 is exactly 75∘\displaystyle 75^{\circ}. This corresponds to Option B.\n\nHence, **Option B** is the correct answer.

About This Chapter: Statistical Representation of Data

Paper

Paper 3: Quantitative Aptitude

Weightage

2-4 Marks

Key Topics

Data, Frequency Distribution, Graphical Representation

This chapter covers Data, Frequency Distribution, Graphical Representation and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

View Official ICAI Syllabus

Exam Strategy Tip

This topic carries 2-4 Marks weightage. Focus on understanding core concepts rather than memorizing.

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