Statistical Description of DataPYQ Jun 23Question 2644 of 295
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The following is the data related to the daily income of 86\displaystyle 86 persons:income in ₹No. of persons:500-999151000-1499281500-1999362000-24997What is the percentage of persons earning at least 1,500\displaystyle 1,500 per day?

Options

A50%\displaystyle 50\%
B45%\displaystyle 45\%
C40%\displaystyle 40\%
D60%\displaystyle 60\%
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Correct Answer

✅ Option a — 50%\displaystyle 50\%

All Options:

  • A50%\displaystyle 50\%
  • B45%\displaystyle 45\%
  • C40%\displaystyle 40\%
  • D60%\displaystyle 60\%

Detailed Solution & Explanation

To find the percentage of persons earning at least ₹1,500\displaystyle 1,500 per day, we analyze the given frequency distribution of daily income for the 86\displaystyle 86 individuals: 1. The income brackets and the corresponding number of persons are: - ₹500\displaystyle 500 to ₹999\displaystyle 999: 15\displaystyle 15 persons - ₹1,000\displaystyle 1,000 to ₹1,499\displaystyle 1,499: 28\displaystyle 28 persons - ₹1,500\displaystyle 1,500 to ₹1,999\displaystyle 1,999: 36\displaystyle 36 persons - ₹2,000\displaystyle 2,000 to ₹2,499\displaystyle 2,499: 7\displaystyle 7 persons 2. "At least ₹1,500\displaystyle 1,500 per day" means an income of ₹1,500\displaystyle 1,500 or more. This condition is satisfied by individuals in the last two brackets: "1500−1999\displaystyle 1500-1999" and "2000−2499\displaystyle 2000-2499". 3. Summing the frequencies of these two brackets, we get the total number of persons earning at least ₹1,500\displaystyle 1,500: Number of Persons=36+7=43 persons\text{Number of Persons} = 36 + 7 = 43\text{ persons} 4. We then calculate this group's percentage relative to the entire sample size of 86\displaystyle 86 persons: Percentage=4386×100%=0.5×100%=50%\text{Percentage} = \frac{43}{86} \times 100\% = 0.5 \times 100\% = 50\% Comparing this result to the given options, we find it matches Option A. Hence, **Option A** is the correct answer.

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