Statistical Description of DataMTP Sep 24 Series IIQuestion 2762 of 295
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In a graphical representation of data, the largest numerical value is 45\displaystyle 45 the smallest numerical value is 25\displaystyle 25. If classes desired are 4\displaystyle 4 then which class interval is

Options

A4.5\displaystyle 4.5
B5\displaystyle 5
C20\displaystyle 20
D7.5\displaystyle 7.5
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Correct Answer

✅ Option b — 5\displaystyle 5

All Options:

  • A4.5\displaystyle 4.5
  • B5\displaystyle 5
  • C20\displaystyle 20
  • D7.5\displaystyle 7.5

Detailed Solution & Explanation

To determine the size of the class interval (width w\displaystyle w) for grouping a dataset, we use the following relationship: 1. **Find the Range** of the data, which is the difference between the largest and smallest values: Largest Value=45\text{Largest Value} = 45 Smallest Value=25\text{Smallest Value} = 25 Range=45−25=20\text{Range} = 45 - 25 = 20 2. **Divide the Range by the number of desired classes** (k=4\displaystyle k = 4) to find the class interval length (w\displaystyle w): w=RangeNumber of Classes=204=5w = \frac{\text{Range}}{\text{Number of Classes}} = \frac{20}{4} = 5 Thus, the class interval size required is 5\displaystyle 5. This corresponds to Option B. Hence, **Option B** is the correct answer.

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