Statistical Representation of DataMCQPYQ June 22Question 2770 of 295
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The following data relate to the marks of 48\displaystyle 48 students in Statistics:56\displaystyle 56 10\displaystyle 10 58\displaystyle 58 38\displaystyle 38 21\displaystyle 21 43\displaystyle 43 12\displaystyle 12 \displaystyle 22<span class="katex-error" title="ParseError: KaTeX parse error: Can&#x27;t use function &#x27;' in math mode at position 3: 48\displaystyle ̲51\displaystyle 39\displaystyle 24\displaystyle …" style="color:#cc0000">48 51\displaystyle 51 39\displaystyle 39 24\displaystyle 24 17\displaystyle 17 36\displaystyle 36 19</span>48\displaystyle 19</span>48 36\displaystyle 36 15\displaystyle 15 33\displaystyle 33 30\displaystyle 30 62\displaystyle 62 57\displaystyle 57 \displaystyle 17<span class="katex-error" title="ParseError: KaTeX parse error: Can&#x27;t use function &#x27;' in math mode at position 2: 5\displaystyle ̲17\displaystyle 45\displaystyle 46\displaystyle …" style="color:#cc0000">5 17\displaystyle 17 45\displaystyle 45 46\displaystyle 46 43\displaystyle 43 55\displaystyle 55 57\displaystyle 57 38</span>43\displaystyle 38</span>43 28\displaystyle 28 32\displaystyle 32 35\displaystyle 35 54\displaystyle 54 27\displaystyle 27 17\displaystyle 17 16\displaystyle 1611\displaystyle 11 43\displaystyle 43 45\displaystyle 45 2\displaystyle 2 16\displaystyle 16 46\displaystyle 46 28\displaystyle 28 45\displaystyle 45What are the frequency densities for the class intervals 2030,3040,4050,5059\displaystyle 20-30, 30-40, 40-50, 50-59?

Options

A0.20,0.50,0.90\displaystyle 0.20, 0.50, 0.90
B0.70,0.90,1.10\displaystyle 0.70, 0.90, 1.10
C0.1875,0.1667,0.2083\displaystyle 0.1875, 0.1667, 0.2083
D0.9,1.10,0.7\displaystyle 0.9, 1.10, 0.7
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Correct Answer

Option d0.9,1.10,0.7\displaystyle 0.9, 1.10, 0.7

All Options:

  • A0.20,0.50,0.90\displaystyle 0.20, 0.50, 0.90
  • B0.70,0.90,1.10\displaystyle 0.70, 0.90, 1.10
  • C0.1875,0.1667,0.2083\displaystyle 0.1875, 0.1667, 0.2083
  • D0.9,1.10,0.7\displaystyle 0.9, 1.10, 0.7

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Detailed Solution & Explanation

To find the frequency density of any class interval, we use the formula:\nFrequency Density=Class FrequencyClass Length\text{Frequency Density} = \frac{\text{Class Frequency}}{\text{Class Length}}\n\nLet's analyze the given dataset of marks:\n`[56, 10, 58, 38, 21, 43, 12, 22, 48, 51, 39, 24, 17, 36, 19, 48, 36, 15, 33, 30, 62, 57, 17, 5, 17, 45, 46, 43, 55, 57, 38, 43, 28, 32, 35, 54, 27, 17, 16, 11, 43, 45, 2, 16, 46, 28, 45]`\n\nLet's count the frequency (f\displaystyle f) for each of the requested class intervals of width 10\displaystyle 10 (using exclusive conventions or boundary approximations):\n1. For the interval **3040\displaystyle 30 - 40** (or 3039\displaystyle 30-39):\n - The matching data points are: 38,39,36,36,33,30,38,32,35\displaystyle 38, 39, 36, 36, 33, 30, 38, 32, 35.\n - Frequency (f\displaystyle f) = 9\displaystyle 9\n - Class Length (L\displaystyle L) = 10\displaystyle 10\n - Frequency Density = 910=0.90\displaystyle \frac{9}{10} = 0.90\n\n2. For the interval **4050\displaystyle 40 - 50** (or 4049\displaystyle 40-49):\n - The matching data points are: 43,48,48,45,46,43,43,43,45,46,45\displaystyle 43, 48, 48, 45, 46, 43, 43, 43, 45, 46, 45.\n - Frequency (f\displaystyle f) = 11\displaystyle 11\n - Class Length (L\displaystyle L) = 10\displaystyle 10\n - Frequency Density = 1110=1.10\displaystyle \frac{11}{10} = 1.10\n\n3. For the interval **5060\displaystyle 50 - 60** (or 5059\displaystyle 50-59):\n - The matching data points are: 56,58,51,57,55,57,54\displaystyle 56, 58, 51, 57, 55, 57, 54.\n - Frequency (f\displaystyle f) = 7\displaystyle 7\n - Class Length (L\displaystyle L) = 10\displaystyle 10\n - Frequency Density = 710=0.70\displaystyle \frac{7}{10} = 0.70\n\nThus, the frequency densities for the intervals 3040,4050,5060\displaystyle 30-40, 40-50, 50-60 are **0.90,1.10,0.70\displaystyle 0.90, 1.10, 0.70**. This corresponds to Option D.\n\nHence, **Option D** 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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