Q.27
ICAR AIEEA PG 2024 - Statistical Sciences
MCQ (Single Correct) +4 −1
English हिन्दी
Which one of the following is a correct statement?

निम्नलिखित में से कौन-सा कथन सही है?
[Note: NTA Official Final Answer Key accepted both Option 1 and Option 2 as correct responses]
[नोट: एनटीए की अंतिम उत्तर कुंजी में विकल्प 1 और विकल्प 2 दोनों को सही माना गया है]

EXPLANATION Measures of Central Tendency: Arithmetic Mean, Geometric Mean, Harmonic Mean, Median and Mode

For a normal distribution, standard empirical relationships link Quartile Deviation (QD), Mean Deviation (MD), and Standard Deviation (SD / $\sigma$):

  • $\text{Mean Deviation} = \sqrt{\frac{2}{\pi}}\sigma \approx 0.7979\sigma \approx \frac{4}{5}\sigma \implies 5 \times \text{MD} = 4 \times \text{SD}$ (Option 1 is correct).
  • $\text{Quartile Deviation} = 0.6745\sigma \approx \frac{2}{3}\sigma \implies 3 \times \text{QD} = 2 \times \text{SD}$ (Option 2 is correct).
    The overall ratio of dispersion measures is: $$\text{QD} : \text{MD} : \text{SD} = \frac{2}{3}\sigma : \frac{4}{5}\sigma : \sigma = 10 : 12 : 15$$
    Because both Option 1 and Option 2 are mathematically and practically valid for a normal distribution, NTA's official final answer key correctly recognized both '1' and '2' as valid answers.

प्रसामान्य बंटन (Normal distribution) के लिए विक्षेपण के मापों के मध्य मानक संबंध:

  • $\text{माध्य विचलन (MD)} \approx \frac{4}{5} \times \text{मानक विचलन (SD)} \implies 5 \times \text{MD} = 4 \times \text{SD}$ (विकल्प 1 सही है)।
  • $\text{चतुर्थक विचलन (QD)} \approx \frac{2}{3} \times \text{मानक विचलन (SD)} \implies 3 \times \text{QD} = 2 \times \text{SD}$ (विकल्प 2 सही है)।
    इनका पारस्परिक अनुपात $QD : MD : SD = 10 : 12 : 15$ होता है।
    चूँकि विकल्प 1 और विकल्प 2 दोनों गणितीय रूप से सही हैं, इसलिए NTA ने आधिकारिक उत्तर कुंजी में दोनों (1 तथा 2) को सही उत्तर स्वीकार किया है।
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