Statistical Representation of DataMCQMTP Dec 2023 Series IIQuestion 2670 of 295
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A student marks in five subjects $53, 54, 55, 84\displaystyle and $89 are $86, 79, 90, 88\displaystyle and $89. If we need to draw a pie chart to represent these marks, what will be central angle for $53$.

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option b — $75^\circ$

All Options:

  • A$105.6^\circ$
  • B$75^\circ$
  • C$103.2^\circ$
  • D$94.8^\circ$

Detailed Solution & Explanation

To find the central angle in a pie chart representing these marks, let's analyze the given data: - Let the set of subjects be {53,54,55,84,89}\displaystyle \{53, 54, 55, 84, 89\}. - The corresponding marks obtained in these five subjects are: - Subject $53\displaystyle : $86 marks - Subject $54\displaystyle : $79 marks - Subject $55\displaystyle : $90 marks - Subject $84\displaystyle : $88 marks - Subject $89\displaystyle : $89 marks - Compute the total marks obtained in all subjects: Total Marks=86+79+90+88+89=432Total Marks=86+79+90+88+89=432\displaystyle \text{Total Marks} = 86 + 79 + 90 + 88 + 89 = 432 - In a pie chart, the total degrees are $360^\circ$. The central angle for any subject is given by the formula: Central Angle=(Marks in SubjectTotal Marks)×360∘\displaystyle \text{Central Angle} = \left( Marks in SubjectTotal Marks\displaystyle \frac{\text{Marks in Subject}}{\text{Total Marks}} \right) ×\displaystyle \times 360^\circ - Let's analyze the options: - For Subject $53\displaystyle (with $86 marks): Central Angle=(86432)×360∘=861.2≈71.67∘\displaystyle \text{Central Angle} = \left( 86432\displaystyle \frac{86}{432} \right) ×\displaystyle \times 360^\circ = 861.2\displaystyle \frac{86}{1.2} ≈\displaystyle \approx 71.67^\circ This value does not match any of the given options: $105.6^\circ\displaystyle , $75^\circ, $103.2^\circ\displaystyle , or $94.8^\circ. - For Subject $55\displaystyle (with $90 marks): Central Angle=(90432)×360∘=901.2=75∘\displaystyle \text{Central Angle} = \left( 90432\displaystyle \frac{90}{432} \right) ×\displaystyle \times 360^\circ = \displaystyle \frac{90}{1.2} = 75^\circ This matches **Option B** exactly. - Thus, there is a typographical error in the question text asking for the central angle of subject $53$ instead of subject $55$. Based on the intended calculation for subject $55\displaystyle to match the standard answer key and options, the central angle is $75^\circ. Hence, **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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