Question

5. 450 छात्रों के सांख्यिकी तथा अर्थशास्त्र में परीक्षा के अंक दिए गए हैं। प्रतीपगमन रेखाएं ज्ञात कीजिए। सांख्यिकी में जिस छात्र ने 50 अंक पाये हैं उसके अर्थशास्त्र के अंक ज्ञात कीजिए: The following data based on 450 students are given for marks in Statistics and Economics at a certain examination. Estimate the average marks in Economics of the candidates who obtained 50 marks in Statistics : सांख्यिकी (Statistics)) अर्थशास्त्र (Economics) औसत अंक (Mean Marks) 40 48 प्रमाप विचलन (Standard Deviation) 12 16 संगत माध्यों से लिए गए विचलनों के गुणनफलों का योग = 42075. Sum of products of deviations of marks from their respective mean = 42075.​

Answer 1

Answer:

what can I help you please tell me

Answer 2

Given : 450 students are given for marks in Statistics and Economics at a certain examination.

Statistics Mean marks = 40

Economics Mean marks = 48

Statistic Standard Deviation = 12

Economics standard deviation = 16

Sum of products of deviations of marks from their respective mean = 42075.​

To Find :  Estimate the average marks in Economics of the candidates who obtained 50 marks in Statistics

Solution:

Statistics marks = x

Economics marks = y

Regression equation of x on y

$x-\overline{x}=r\dfrac{\sigma_x}{\sigma_y}( y-\overline{y})$

$r=\dfrac{\sum d_x.d_y}{n\sigma_x.\sigma_y}$

$\sum d_x.d_y = 42075, n=450, \sigma_x=12,\sigma_y=16$

=> r  = 42075/(450 * 12 * 16)

=> r ≈ 0.487

$x-\overline{x}=r\dfrac{\sigma_x}{\sigma_y}( y-\overline{y})$

$\overline{x}= 40, \overline{y}=48$

x - 40  = 0.487 (12 / 16) (y - 48)

=> x - 40  = 0.365(y - 48)

=> x  = 0.365y + 22.469

As value of x is given and we need to find y

so

Regression equation of y on x

$y-\overline{y}=r\dfrac{\sigma_y}{\sigma_x}( x-\overline{x})$

y - 48  =  0.487 ( 16/12) (x - 40)

=> y - 48  = 0.6493 (x - 40)

=> y - 48 = 0.6493x  - 25.97

=> y = 0.6493x  + 22.03

x = 50

=> y =  54.495

=> y  ≈ 54.5

the average marks in Economics of the candidates who obtained 50 marks in Statistics :   54.5

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