Question 12 Marks
For a sample data collected to know the relation between number of customers and sales $($thousand $₹)$ visiting a mall, the ranks are as follows.
| Rank for number of customers $R_{(x)}$ |
$6$ |
$4.5$ |
$3$ |
$4.5$ |
$1$ |
$2$ |
Rank for sales
$($thousand $₹) R_{(y)}$ |
$4.5$ |
$4.5$ |
$2.5$ |
$6$ |
$1$ |
$2.5$ |
Calculate the rank correlation coefficient. View full question & answer→Question 22 Marks
For $9$ observations of a bivariate data, the sum of squares of differences in their ranks is $96 .$ Find the rank correlation coefficient.
View full question & answer→Question 32 Marks
If $\sum_1^{12}\left(R_x-R_y\right)^2=90$, find Spearman's correlation coefficient.
View full question & answer→Question 42 Marks
The coefficient of rank correlation between two related variables was found to be $0.5$. If the number of pairs of observations is $8 ,$ find sum of squares of differences of ranks.
View full question & answer→Question 52 Marks
The coefficient of rank correlation between two related variables was found to be $-1$. If $n=10$, find $\Sigma d^2$.
View full question & answer→Question 62 Marks
$15$ contestants are ranked by two judges in an elocution competition and the sum of squares of differences in their ranks is found to be $250 .$ Find the correlation coefficient.
View full question & answer→Question 72 Marks
For $8$ observations of a bivariate data, $r=0.75$. If $\quad \bar{x}=7, \bar{y}=5, S_x=5$ and $\Sigma(y-\bar{y})^2=128$, find $\Sigma x y$.
View full question & answer→Question 82 Marks
If $n=20, \Sigma x y=5000, \bar{x}=15, \bar{y}=10, S_x=12$ and $S_y=10$ find $r$ :
View full question & answer→Question 92 Marks
If $\Sigma x y=8000, n=10, \bar{x}=30, \bar{y}=20, S_x=25$ and $S_y=12$, find the value of correlation coefficient.
View full question & answer→Question 102 Marks
For two random variables $X$ and $Y$, if correlation coefficient $=-\frac{3}{4}$, variance of $X=324$, standard deviation of $Y=20$ and number of observations $=5$, find the sum of the product of the deviations taken from the means of $X$ and $Y$.
Answer$\Sigma(x-\bar{x})(y-\bar{y})=-1350$
View full question & answer→Question 112 Marks
If $n=8, s_y=10, \Sigma(x-\bar{x})(y-\bar{y})=-240$ and $\Sigma(x-\bar{x})^2=200$, find the value of $r$.
View full question & answer→Question 122 Marks
If $n=10, r=0.8, s_y^2=25$ and $\Sigma(x-\bar{x})(y-\bar{y})=480$, find the standard deviation of $X$.
View full question & answer→Question 132 Marks
If $n=30, r=0.5, \Sigma(x-\bar{x})(y-\bar{y})=900$ and $s_x^2=100$, find the standard deviation of $Y$.
View full question & answer→Question 142 Marks
For a sample data of ten observations, the sum of product of deviations taken from mean $=120$, variance of $X=36$ and variance of $Y=25$. Find the correlation coefficient.
View full question & answer→Question 152 Marks
If $n=4, r=0.4, \operatorname{Cov}(x, y)=4 S_y$ and $S_x=2 S_y$, find the variance of $X$.
View full question & answer→Question 162 Marks
If $n=6, r=0.8, \operatorname{Cov}(x, y)=80$ and $S_y=8$, find the variance of $X$,
View full question & answer→Question 172 Marks
If $n=10, \operatorname{Cov}(x, y)=30, s_x=10$ and $s_y^2=36$, find the value of $r$
View full question & answer→Question 182 Marks
Find the correlation coefficient from the following data for $15$ observations of two random variables $X$ and $Y . \quad \Sigma(x-\bar{x})(y-\bar{y})=-60, \quad \Sigma(x-\bar{x})^2=100$ and $\Sigma(y-\bar{y})^2=64$
View full question & answer→Question 192 Marks
From the following data related to two random variables $X$ and $Y$, draw a scatter diagram and interpret it.
| $x$ |
$10$ |
$20$ |
$30$ |
$40$ |
$50$ |
| $y$ |
$5$ |
$4$ |
$3$ |
$2$ |
$1$ |
View full question & answer→Question 202 Marks
From the following data related to two random variables $X$ and $Y$, draw a scatter diagram and interpret it.
| $x$ |
$3$ |
$6$ |
$9$ |
$12$ |
$15$ |
| $y$ |
$4$ |
$5$ |
$6$ |
$7$ |
$8$ |
View full question & answer→Question 212 Marks
Which precautions should be taken in the interpretation of correlation coefficient ?
Question 222 Marks
Write the merits of Spearman's rank correlation method.
Question 232 Marks
Write the formula in detail, used to find rank correlation coefficient when there is a tie in the observations.
Question 242 Marks
Which correlation coefficient is more reliable between Karl Pearson's correlation coefficient and Spearman's correlation coefficient? Why?
Question 252 Marks
Write the limitations of Karl Pearson's method.
Question 262 Marks
Write the characteristics of correlation coefficient.
Question 272 Marks
Write the merits of scatter diagram method.