Statistical Representation of DataMCQMTP Dec 2023 Series IIQuestion 2756 of 295
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From the following data 73,72,65,41,54,80,50,46,49,53\displaystyle 73, 72, 65, 41, 54, 80, 50, 46, 49, 53, find the number of class intervals if class length is given as 5\displaystyle 5

Options

A6\displaystyle 6
B8\displaystyle 8
C7\displaystyle 7
D5\displaystyle 5
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Correct Answer

✅ Option b — 8\displaystyle 8

All Options:

  • A6\displaystyle 6
  • B8\displaystyle 8
  • C7\displaystyle 7
  • D5\displaystyle 5

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Detailed Solution & Explanation

To find the number of class intervals required for a dataset, we first determine the range of the data and then divide by the class length: 1. **Identify the minimum and maximum values** in the dataset: Data:73,72,65,41,54,80,50,46,49,53\text{Data}: 73, 72, 65, 41, 54, 80, 50, 46, 49, 53 - Minimum value=41\displaystyle \text{Minimum value} = 41 - Maximum value=80\displaystyle \text{Maximum value} = 80 2. **Calculate the Range**: Range=Maximum Value−Minimum Value=80−41=39\text{Range} = \text{Maximum Value} - \text{Minimum Value} = 80 - 41 = 39 3. **Calculate the number of class intervals (k\displaystyle k)** using the given class length of 5\displaystyle 5: k=RangeClass Length=395=7.8k = \frac{\text{Range}}{\text{Class Length}} = \frac{39}{5} = 7.8 Since the number of class intervals must be a whole number to fully cover all data points, we round up 7.8\displaystyle 7.8 to the next integer, which is 8\displaystyle 8. For example, starting the classes at 41\displaystyle 41, we would have: 41−45,46−50,51−55,56−60,61−65,66−70,71−75,76−80\displaystyle 41-45, 46-50, 51-55, 56-60, 61-65, 66-70, 71-75, 76-80, which is exactly 8\displaystyle 8 intervals. 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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