Statistical Representation of DataMCQMTP Nov 19Question 2773 of 295
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The width of each of ten classes in a frequency distribution is $2.5$ and the lower class boundary of the lowest class is $10.6$. Which one of the following is the upper class boundary of the highest class?

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

✅ Option a — $35.6$

All Options:

  • A$35.6$
  • B$33.1$
  • C$30.6$
  • DNone of these

Detailed Solution & Explanation

We are given the following characteristics of a continuous grouped frequency distribution:\n- Number of class intervals, n=10\displaystyle n = 10\n- Width of each class interval, w=2.5\displaystyle w = 2.5\n- Lower class boundary of the lowest (10th or first) class, LCB1=10.6\displaystyle LCB_1 = 10.6\n\nSince the class intervals are contiguous (continuous with no gaps between them), the total width spanned by all $10classesistheproductofthenumberofclassesandtheclasswidth:\n<spanclass="katex−display"><spanclass="katex"><spanclass="katex−mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"display="block"><semantics><mrow><mtext>Total Spanned Width</mtext><mo>=</mo><mi>n</mi><mo>×</mo><mi>w</mi><mo>=</mo><mn>10</mn><mo>×</mo><mn>2.5</mn><mo>=</mo><mn>25</mn></mrow><annotationencoding="application/x−tex">Total Spanned Width=n×w=10×2.5=25</annotation></semantics></math></span><spanclass="katex−html"aria−hidden="true"><spanclass="base"><spanclass="strut"style="height:0.8889em;vertical−align:−0.1944em;"></span><spanclass="mordtext"><spanclass="mord">Total Spanned Width</span></span><spanclass="mspace"style="margin−right:0.2778em;"></span><spanclass="mrel">=</span><spanclass="mspace"style="margin−right:0.2778em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.6667em;vertical−align:−0.0833em;"></span><spanclass="mordmathnormal">n</span><spanclass="mspace"style="margin−right:0.2222em;"></span><spanclass="mbin">×</span><spanclass="mspace"style="margin−right:0.2222em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.4306em;"></span><spanclass="mordmathnormal"style="margin−right:0.02691em;">w</span><spanclass="mspace"style="margin−right:0.2778em;"></span><spanclass="mrel">=</span><spanclass="mspace"style="margin−right:0.2778em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.7278em;vertical−align:−0.0833em;"></span><spanclass="mord">10</span><spanclass="mspace"style="margin−right:0.2222em;"></span><spanclass="mbin">×</span><spanclass="mspace"style="margin−right:0.2222em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.6444em;"></span><spanclass="mord">2.5</span><spanclass="mspace"style="margin−right:0.2778em;"></span><spanclass="mrel">=</span><spanclass="mspace"style="margin−right:0.2778em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.6444em;"></span><spanclass="mord">25</span></span></span></span></span>\n\nTheupperclassboundaryofthehighest(10th)class(\displaystyle classes is the product of the number of classes and the class width:\n<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mtext>Total Spanned Width</mtext><mo>=</mo><mi>n</mi><mo>×</mo><mi>w</mi><mo>=</mo><mn>10</mn><mo>×</mo><mn>2.5</mn><mo>=</mo><mn>25</mn></mrow><annotation encoding="application/x-tex">Total Spanned Width=n\displaystyle \text{Total Spanned Width} = n ×\displaystyle \times w = 10 ×\displaystyle \times 2.5 = 25</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord text"><span class="mord">Total Spanned Width</span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal" style="margin-right:0.02691em;">w</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">10</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">2.5</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">25</span></span></span></span></span>\n\nThe upper class boundary of the highest (10th) class (UCB_{10}$) will be the lower class boundary of the first class plus this total spanned width:\nUCB10=LCB1+Total Spanned Width=10.6+25=35.6UCB_{10} = LCB_1 + Total Spanned Width=10\displaystyle \text{Total Spanned Width} = 10.6 + 25 = 35.6\n\nThis matches Option A.\n\nHence, **Option A** 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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