Tag: karl's pearson method

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Questions Related to karl's pearson method

Multiple choice statistics skewness of frequency distribution karl pearson coefficient of correlation karl pearson's product moment method karl's pearson method

Karl Pearson's coefficient of skewness of a distribution is 0.32.Its s.d.is 6.5 and mean is 29.6.The mode and median of the distribution are

  1. 27.52,28.91

  2. 26.92,27.23

  3. 25.67,26.34

  4. none of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Karl Pearson's coefficient of skewness $\displaystyle =\frac{Mean-Mode}{S.D.}$ $\displaystyle \therefore 0.32=\frac{29.6-Mode}{6.5}\Rightarrow Mode=27.52$ Also Karl Pearson's coeff.of skewness $\displaystyle =\frac{3\left ( Mean-Median \right )}{S.D}$ $\displaystyle \because 0.32=\frac{3\left ( 29.6-Median \right )}{6.5}$ $\displaystyle \Rightarrow Median=28.91$

Multiple choice statistics skewness of frequency distribution karl pearson coefficient of correlation karl pearson's product moment method karl's pearson method

The sum of the deviations of the variates 6,8,10,16,20,24 

  1. -1

  2. 1

  3. 0

  4. 4
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\Rightarrow$   $Mean = \dfrac{6+8+10+16+20+24}{6}=14$

$\Rightarrow$   Sum of the deviations = $(6-14)+(8-14)+(10-14)+(16-14)+(20-14)+(24-14)$
$\Rightarrow$   Sum of the deviation = $-8-6-4+2+6+10$
$\therefore$    Sum of the deviation = $-18+18$
$\therefore$    Sum of the deviation = $0$

Multiple choice statistics skewness of frequency distribution karl pearson coefficient of correlation karl pearson's product moment method karl's pearson method

Choose the statement which consists of two correlated variables.

  1. Increase in the intensity of cold results in greater sale of woollen clothes

  2. Increase in temperature of delhi has led to congestion

  3. Increase in weight of children s accompanied by increase in weight of their mother

  4. None of the above
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Since increase in intensity of cold result in greater scale of woolen clothes,

Multiple choice statistics skewness of frequency distribution karl pearson coefficient of correlation karl pearson's product moment method karl's pearson method

Calculate Pearson's coefficient of correlation between the values of $X$ and $Y$.

X 1 2 3 4 5
Y 7 6 5 4 3
  1. $-0.3$
  2. $0.3$
  3. $1$
  4. $-1$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
$X\\ 1\\ 2\\ 3\\ 4\\ 5\\ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \\ \overline { x } \cfrac { 15 }{ 5 } =3$                $Y\\ 7\\ 6\\ 5\\ 4\\ 3\\ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \\ \overline { y } =\cfrac { 25 }{ 5 } =5$                  $Y=y-\overline { y } \\ \quad 02\\ \quad 01\\ \quad 00\\ -1\\ -1\\ \ _ \ _ \ _ \ _ \ _ \ _ \\ \quad 0$                    $XY\\ -4\\ -1\\ \quad 0\\ -1\\ -4\\ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \\ \sum { XY=-10 } $                 ${ X }^{ 2 }\\ 4\\ 1\\ 0\\ 1\\ 4\\ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \\ \sum { { X }^{ 2 }=10 } $        

${ Y }^{ 2 }\\ 4\\ 1\\ 0\\ 1\\ 4\\ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \\ \sum { { Y }^{ 2 }=10 } $

Therefore, $r=\cfrac { \sum { XY }  }{ \sqrt { \sum { { X }^{ 2 }\sum { { Y }^{ 2 } }  }  }  } \\ =\cfrac { -10 }{ \sqrt { 10*10 }  } \\ =\cfrac { -10 }{ 10 } \\ =-1.$
Multiple choice statistics skewness of frequency distribution karl pearson coefficient of correlation karl pearson's product moment method karl's pearson method

For $ n=25,\sum x=125,\sum x^2=650,\sum y=100,\sum y^2=460,\sum xy=508$, correlation coefficient is 

  1. $0.99$
  2. $0.207$
  3. $0.66$
  4. $0.89$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$n=25$

$\sum x=125,\ \sum{{x}^{2}}=650,\ \sum{xy}=334$  $\sum y=100,\ \sum{{y}^{2}}=508$
$r=\cfrac { n\sum { xy } -(\sum { x } \times \sum { y } ) }{ \sqrt { (n\sum { { x }^{ 2 } } -\sum { { x }^{ 2 } } )(n\sum { { y }^{ 2 } } -\sum { { y }^{ 2 } } ) }  } =\cfrac { 25\times 508 -100\times 125 }{ \sqrt { (25\times 650 -{ 125 }^{ 2 }  )(25\times 460 -{100}^{2}) }  }=0.207 $

Multiple choice statistics skewness of frequency distribution karl pearson coefficient of correlation karl pearson's product moment method karl's pearson method

$n=25,\sum x=125,\sum x^2=650, \sum y=100,\sum y^2=460,\sum xy=508$. It was observed that two pair of values of $(x,y)$ were copied as $ (6,14)$ and $(8,6) $ instead of $(8,12),(6,8).$ The correct correlation coefficient is 

  1. $0.667$
  2. $0.87$
  3. $-0.25$
  4. $0.356$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Corrected $\sum x=125-6-8+8+6=125$

Corrected $\sum y=100-14-6+12+8=100$
Corrected $\sum x^2=650-(6)^2-(8)^2+(6)^2+(8)^2=650$
Corrected $\sum y^2=460-(14)^2-(6)^2+(12)^2+(8)^2=436$
Corrected $\sum xy=508-6\times 18-8\times 6+8\times 12+6\times 8=520$
The formula for Pearson product moment correlation is
$r=\dfrac{n\sum xy-(\sum x)(\sum y)}{\sqrt{[n\sum x^2-(\sum x)^2][n\sum y^2-(\sum y)^2]}}$

    $=\dfrac{25\times 520-125\times 100}{\sqrt{[25\times 650-(125)^2][25\times 436-(100)^2]}}$

   $=\dfrac{13000-12500}{\sqrt{[16250-15625][10900-10000]}}$

   $=\dfrac{500}{\sqrt{[625][900]}}$

   $=\dfrac{500}{(25)(30)}$

   $=\dfrac{2}{3}$

   $=0.667$

Multiple choice statistics skewness of frequency distribution karl pearson coefficient of correlation karl pearson's product moment method karl's pearson method

The coefficient of correlation when coefficients of regression are $0.2$ and $1.8$ is

  1. $0.36$
  2. $0.2$
  3. $0.6$
  4. $0.9$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$Given\quad { b } _{ xy }=0.2\\ { b } _{ yx }=0.8\\ r=\sqrt { { b } _{ xy }\times { b } _{ yx } } \\ r=\sqrt { 0.36 } \\ r=0.6$

Where r is coefficient of correlation.

Multiple choice business maths correlation and regression analysis karl pearson coefficient of correlation karl pearson's product moment method karl's pearson method

Standard error of regression analysis is classified as

  1. average of coefficient

  2. variance of residual

  3. mean of residual

  4. average of residual
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Standard error of regression analysis is classified as variance of residuals.

Variance of residuals also known as error variance.

Multiple choice business maths correlation and regression analysis karl pearson coefficient of correlation karl pearson's product moment method karl's pearson method

The independent variable is also called: 

  1. Regressor

  2. Regressand

  3. Predictand

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A linear regression line has an equation of the form $Y=a+bX$


where $Y$ is called dependent variable or response or regressand
$X$ is called independent variable or predictors or explanatory variable or regressor
$a$ is the y-intercept and
$b$ is the slope of the line.