Statistical Description of DataPYQ Dec. 23Question 2772 of 295
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Consider the following data where class length is given as 5\displaystyle 5. Calculate the number of class intervals 59,68,78,57,44,73,40,60,70,47\displaystyle 59, 68, 78, 57, 44, 73, 40, 60, 70, 47.

Options

A5\displaystyle 5
B6\displaystyle 6
C7\displaystyle 7
D8\displaystyle 8
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Correct Answer

✅ Option d — 8\displaystyle 8

All Options:

  • A5\displaystyle 5
  • B6\displaystyle 6
  • C7\displaystyle 7
  • D8\displaystyle 8

Detailed Solution & Explanation

To determine the number of class intervals needed to group a given dataset, we use the values to find the range:\n\n1. **Identify the minimum and maximum values** in the dataset:\n Dataset:59,68,78,57,44,73,40,60,70,47\text{Dataset}: 59, 68, 78, 57, 44, 73, 40, 60, 70, 47\n - Minimum Value=40\displaystyle \text{Minimum Value} = 40\n - Maximum Value=78\displaystyle \text{Maximum Value} = 78\n\n2. **Calculate the Range**:\n Range=Maximum Value−Minimum Value=78−40=38\text{Range} = \text{Maximum Value} - \text{Minimum Value} = 78 - 40 = 38\n\n3. **Calculate the number of class intervals (k\displaystyle k)** with class length 5\displaystyle 5:\n k=RangeClass Length=385=7.6k = \frac{\text{Range}}{\text{Class Length}} = \frac{38}{5} = 7.6\n\nSince the number of classes must be an integer to completely cover all data points from 40\displaystyle 40 to 78\displaystyle 78, we round up 7.6\displaystyle 7.6 to the next whole number, which is 8\displaystyle 8. \nIf we construct the classes starting from 40\displaystyle 40, the intervals of length 5\displaystyle 5 are: 40−44,45−49,50−54,55−59,60−64,65−69,70−74,75−79\displaystyle 40-44, 45-49, 50-54, 55-59, 60-64, 65-69, 70-74, 75-79, which is exactly 8\displaystyle 8 class intervals. This corresponds to Option D.\n\nHence, **Option D** is the correct answer.

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