We read your photo as:

Calculate the coefficient of correlation using the provided data and the Pearson product-moment correlation coefficient formula.

Mathematics

ScanSolve AI Answer

Answer

0.9791

Step-by-step solution

7 steps

गुणांक सहसंबंध (coefficient of correlation) की गणना करने के लिए, हम पियर्सन के उत्पाद-क्षण सहसंबंध गुणांक (Pearson product-moment correlation coefficient) सूत्र का उपयोग करेंगे:

r=n∑(XY)−(∑X)(∑Y)[n∑X2−(∑X)2][n∑Y2−(∑Y)2]r = \frac{n \sum (XY) - (\sum X)(\sum Y)}{\sqrt{[n \sum X^2 - (\sum X)^2][n \sum Y^2 - (\sum Y)^2]}}

जहाँ nn डेटा बिंदुओं की संख्या है।

  1. आवश्यक योगों की गणना करें।

    यहाँ n=5n=5 डेटा बिंदु हैं।

    XYXYX^2Y^2
    2714449
    3927981
    4104016100
    5147025196
    6159036225
    --------------------
    ∑X=20\sum X = 20∑Y=55\sum Y = 55∑XY=241\sum XY = 241∑X2=90\sum X^2 = 90∑Y2=651\sum Y^2 = 651

  2. सूत्र में मानों को प्रतिस्थापित करें।

    r=5(241)−(20)(55)[5(90)−(20)2][5(651)−(55)2]r = \frac{5(241) - (20)(55)}{\sqrt{[5(90) - (20)^2][5(651) - (55)^2]}}

  3. अंश (numerator) की गणना करें।

    5(241)−(20)(55)=1205−1100=1055(241) - (20)(55) = 1205 - 1100 = 105

  4. हर (denominator) के पहले भाग की गणना करें।

    5(90)−(20)2=450−400=505(90) - (20)^2 = 450 - 400 = 50

  5. हर के दूसरे भाग की गणना करें।

    5(651)−(55)2=3255−3025=2305(651) - (55)^2 = 3255 - 3025 = 230

  6. हर की गणना करें।

    (50)(230)=11500≈107.238\sqrt{(50)(230)} = \sqrt{11500} \approx 107.238

  7. गुणांक सहसंबंध (rr) की गणना करें।

    r=105107.2380529r = \frac{105}{107.2380529} r≈0.97914r \approx 0.97914

    गुणांक सहसंबंध है:

    0.97910.9791
Was this helpful?

Try one yourself

A new problem that tests the same skill.

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question

More Mathematics Questions

QCalculate the Pearson product-moment correlation coefficient (r) and find the variance and standard…QCalculate the product-moment correlation coefficient r and the least squares regression line of Y on…QTo calculate Pearson's correlation coefficient (r), we first need to complete the table with x2, y2…QCalculate the rank correlation coefficient using Spearman's formula, given the ranks of two methods.QCalculate the Spearman Rank Order Correlation coefficient for the given pretest and posttest scores…
Browse by topic:Statistics
See all Mathematics questions →
Got a syllabus? Photograph it and I'll tell you what's due and what's worth the most.
Handwritten step-by-step solution preview

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp