Statistical Description of DataMTP Dec 2023 Series IIQuestion 2757 of 295
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The number of observations between 150\displaystyle 150 and 200\displaystyle 200 based on the following data is:Value | No of observations--- | ---More than 100\displaystyle 100 | 70\displaystyle 70More than 150\displaystyle 150 | 63\displaystyle 63More than 200\displaystyle 200 | 28\displaystyle 28More than 250\displaystyle 250 | 05\displaystyle 05

Options

A46\displaystyle 46
B35\displaystyle 35
C28\displaystyle 28
D23\displaystyle 23
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Correct Answer

✅ Option b — 35\displaystyle 35

All Options:

  • A46\displaystyle 46
  • B35\displaystyle 35
  • C28\displaystyle 28
  • D23\displaystyle 23

Detailed Solution & Explanation

The given table represents a 'more than' cumulative frequency distribution: - The number of observations with values greater than 150\displaystyle 150 is 63\displaystyle 63. - The number of observations with values greater than 200\displaystyle 200 is 28\displaystyle 28. To find the number of observations that fall specifically in the interval between 150\displaystyle 150 and 200\displaystyle 200 (i.e., greater than 150\displaystyle 150 but less than or equal to 200\displaystyle 200), we subtract the cumulative frequency of the higher value from the cumulative frequency of the lower value: Number of observations (150<x≤200)=Frequency(>150)−Frequency(>200)\text{Number of observations } (150 < x \le 200) = \text{Frequency}(> 150) - \text{Frequency}(> 200) Number of observations (150<x≤200)=63−28=35\text{Number of observations } (150 < x \le 200) = 63 - 28 = 35 Thus, there are 35\displaystyle 35 observations between 150\displaystyle 150 and 200\displaystyle 200. This corresponds to Option B. Hence, **Option B** is the correct answer.

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