Which of the following statements is true? | Agrigyan

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RPSC Assistant Agriculture Officer 2018

MCQ (Single Correct)

Which of the following statements is true?

निम्नलिखित में से कौन सा कथन सत्य है?

Standard deviation is square of variance. मानक विचलन प्रसरण का वर्ग होता है। Variance is not independent of change of origin of the data. आँकड़ों के मूल में परिवर्तन से प्रसरण स्वतन्त्र नहीं होता है। Measure of relative dispersion is coefficient of variation. सापेक्ष विक्षेपण का माप विचलन गुणांक होता है। Covariance is measured between more than two variables. सह-प्रसरण दो से ज्यादा चरों के बीच ज्ञात किया जाता है।

Measures of dispersion are classified into absolute measures (Range, Quartile Deviation, Mean Deviation, Standard Deviation) and relative measures (Coefficients).
The Coefficient of Variation ($CV = \frac{\sigma}{\bar{x}} \times 100$) developed by Karl Pearson is the standard relative measure of dispersion, expressed as a pure percentage free from units of measurement to compare consistency across distributions.
Statement 1 is false because variance is the square of standard deviation ($\text{Var} = \sigma^2$), not vice versa.
Statement 2 is false because variance is independent of change of origin; Statement 4 is false because covariance measures linear association between exactly two variables.

विक्षेपण की मापों को दो वर्गों में विभाजित किया जाता है: निरपेक्ष माप (जैसे प्रमाप विचलन, प्रसरण, परिसर) तथा सापेक्ष माप (विचरण गुणांक आदि)।
कार्ल पियर्सन द्वारा प्रतिपादित विचरण गुणांक (Coefficient of Variation / $CV = \frac{\sigma}{\bar{x}} \times 100$) सापेक्ष विक्षेपण का एक इकाई-रहित मानक माप है, जिसका उपयोग दो श्रेणियों की समरूपता या स्थिरता की तुलना के लिए किया जाता है। अतः कथन 3 सत्य है।
प्रसरण प्रमाप विचलन का वर्ग होता है (कथन 1 गलत है)।
प्रसरण मूल बिंदु के परिवर्तन से स्वतंत्र होता है (कथन 2 गलत है) तथा सह-प्रसरण केवल दो चरों के बीच ज्ञात होता है।

Explanation not matching this question? क्या व्याख्या इस प्रश्न से मेल नहीं खा रही? Report

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