Statistical Description of DataMTP 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

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.

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