Question 1 : The marks in history and mathematics of twelve students in a public examination are given below. Calculate a coefficient of correlation by ranks.<br><table class="wysiwyg-table"><tbody><tr><td>Student</td><td>A</td><td>B</td><td>C</td><td>D</td><td>E</td><td>F</td><td>G</td><td>H</td><td>I</td><td>J</td><td>K</td><td>L</td></tr><tr><td>History</td><td>69</td><td>36</td><td>39</td><td>71</td><td>67</td><td>76</td><td>40</td><td>20</td><td>85</td><td>65</td><td>55</td><td>34</td></tr><tr><td>Mathematics</td><td>33</td><td>52</td><td>71</td><td>25</td><td>79</td><td>22</td><td>83</td><td>81</td><td>24</td><td>35</td><td>46</td><td>64</td></tr></tbody></table><br>
Question 2 :
The regression coefficients of a bivariate distribution are -0.64 and -0.36. Then the correlation coefficient of the distribution is
Question 3 :
For a 12 pair of observations it was found that  $\sum x=30,\ \sum y=5,\sum x^2=670,\sum y^2=285,\sum xy=334$. Find correlation coefficient.
Question 4 :
The coefficient of correlation if $\overline { x } =\overline { y } =0$, $\sum _{ }^{ }{ { x }_{ i }{ y }_{ i }=12 } ,\quad { \sigma }_{ x }=4\quad ,{ \sigma }_{ y }=4$ and $n=10$ is
Question 5 :
For two variables $x$ and $y$ regression equations are given as $7x-3y-18=0$ and $4x-y-11=0$ then the correlation coefficient between $x$ and $y$ is
Question 6 : FInd the rank correlation from the following data:<br><table class="wysiwyg-table"><tbody><tr><td>S. No.</td><td>1</td><td>2</td><td>3</td><td>4</td><td>5</td><td>6</td><td>7</td><td>8</td><td>9</td><td>10</td></tr><tr><td>Rank Differences</td><td>-2</td><td>-4</td><td>-1</td><td>3</td><td>2</td><td>0</td><td>-2</td><td>3</td><td>3</td><td>-2</td></tr></tbody></table>
Question 7 : Following are the rank obtained by 10 students in two subjects , Statistics and Mathematics . To what extent the knowledge of the students in the two subjects is related?<br><table class="wysiwyg-table"><tbody><tr><td>Statistics</td><td>1</td><td>3</td><td>3</td><td>4</td><td>5</td><td>6</td><td>7</td><td>8</td><td>9</td><td>10</td></tr><tr><td>Mathematics</td><td>2</td><td>4</td><td>1</td><td>5</td><td>3</td><td>9</td><td>7</td><td>10</td><td>6</td><td>8</td></tr></tbody></table>
Question 8 :
For two variables x and y. the two regression coefficients are $b_{x}= -\dfrac{3}{2}$ and $b_{y}=-\dfrac{1}{6}$. <br/>The correlation coefficient between x and y is : 
Question 9 : Following are the marks of $10$ students obtained in Physics and Chemistry in an examination. Find the rank-correlation coefficient.<br><table class="wysiwyg-table"><tbody><tr><td>x</td><td>43</td><td>96</td><td>74</td><td>38</td><td>35</td><td>43</td><td>22</td><td>56</td><td>35</td><td>80</td></tr><tr><td>y</td><td>30</td><td>94</td><td>84</td><td>13</td><td>30</td><td>18</td><td>30</td><td>41</td><td>48</td><td>95</td></tr></tbody></table>
Question 10 : Calculate Pearson's coefficient of correlation between the values of $X$ and $Y$.<br><table class="wysiwyg-table"><tbody><tr><td>X</td><td>1</td><td>2</td><td>3</td><td>4</td><td>5</td></tr><tr><td>Y</td><td>7</td><td>6</td><td>5</td><td>4</td><td>3</td></tr></tbody></table>
Question 11 :
If $\displaystyle cov\left( X,Y \right) =1,var\left( X \right) =1,var\left( Y \right) =4$ then $Cor(X,Y)=$
Question 12 :
State the following statement is True or False<br/>If two regression coefficients are $0.8$ and $0.2$ respectively, then correlation coefficient is  equal to zero.<br/>
Question 13 :
The coefficient of correlation when coefficients of regression are $0.2$ and $1.8$ is
Question 14 : <table class="wysiwyg-table"><tbody><tr><td></td><td>Height</td><td>Long Jump</td><td>High Jump</td></tr><tr><td>A</td><td>158</td><td>324</td><td>175</td></tr><tr><td>B</td><td>165</td><td>365</td><td>185</td></tr><tr><td>C</td><td>162</td><td>380</td><td>180</td></tr><tr><td>D</td><td>170</td><td>400</td><td>184</td></tr><tr><td>E</td><td>175</td><td>350</td><td>199</td></tr><tr><td>F</td><td>163</td><td>350</td><td>172</td></tr><tr><td>G</td><td>178</td><td>425</td><td>189</td></tr></tbody></table>Find rank correlation between height & long jump and height & high jump.
Question 15 :
The standard deviation for variables x and y be 3 and 4 respectively and their covariance is 8. then coefficient of correlation between them is<br><br>
Question 17 : Calculate the correlation coefficient between the corresponding values of X and Y in the following table:<br/><table class="wysiwyg-table"><tbody><tr><td>X</td><td>2</td><td>4</td><td>5</td><td>6</td><td>8</td><td>11</td></tr><tr><td>Y</td><td>18</td><td>12</td><td>10</td><td>8</td><td>7</td><td>5</td></tr></tbody></table>
Question 19 :
$n=10,\sum x=55,\sum x^2=385, \sum y=40,\sum y^2=192,\sum (x+y)^2=947$. The correlation coefficient is 
Question 20 :
If $n=10, \sum x=4,\sum y=3, \sum x^2=8,\sum y^2=9$ and $\sum xy=3,$ then the coefficient of $r_{x,y}$ is
Question 21 :
Two variates, x and y, are uncorrelated and have standard deviations $\sigma_x$ and $\sigma_y$ respectively. What is the correlation coefficient between x + y and x - y?
Question 22 :
What is the formula to calculate Spearman's rank correlation coefficient when ranks are not repeated.
Question 23 :
If the covariance between x and y is $30$, variance of x is $25$ and variance of y is $144$, then what is the correlation coefficient?
Question 24 :
The correlation coefficient between two variables $X$ and $Y$ is found to be $0.6$. All the observations on $X$ and $Y$ are transformed using the transformations $U = 2 - 3X$ and $V = 4Y + 1$. The correlation coefficient between the transformed variables $U$ and $V$ will be:
Question 25 : The marks in History and Mathematics of twelve students in a public examination are given below. Calculate a coefficient of correlation by ranks.<br/><table class="wysiwyg-table"><tbody><tr><td>Student</td><td>$A$</td><td>$B$</td><td>$C$</td><td>$D$</td><td>$E$</td><td>$F$</td><td>$G$</td><td>$H$</td><td>$I$</td><td>$J$</td><td>$K$</td><td>$L$</td></tr><tr><td>History</td><td>$69$</td><td>$36$</td><td>$39$</td><td>$71$</td><td>$67$</td><td>$76$</td><td>$40$</td><td>$20$</td><td>$85$</td><td>$65$</td><td>$55$</td><td>$34$</td></tr><tr><td>Mathematics</td><td>$33$</td><td>$52$</td><td>$71$</td><td>$25$</td><td>$79$</td><td>$22$</td><td>$83$</td><td>$81$</td><td>$24$</td><td>$35$</td><td>$46$</td><td><br/>$64$<br/><br/></td></tr></tbody></table>Interpret the result.
Question 28 :
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
Question 29 :
$n=25,\sum x=125,\sum x^2=650, \sum y=100,\sum y^2=460,\sum xy=508$. 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 
Question 30 :
If the value of correlation $ \displaystyle r=\frac{1}{2} $ or $ \displaystyle r= - \frac{1}{2} $, then correlation is called<br>
Question 31 : Calculate the coefficient of correlation between $x$ and $y$ for the data<br><table class="wysiwyg-table"><tbody><tr><td>x</td><td>1</td><td>2</td><td>3</td><td>4</td><td>5</td><td>6</td><td>7</td><td>8</td><td>9</td><td>10</td></tr><tr><td>y</td><td>3</td><td>10</td><td>5</td><td>1</td><td>2</td><td>9</td><td>4</td><td>8</td><td>7</td><td>6</td></tr></tbody></table>
Question 32 : The marks obtained by nine students in Physics and Mathematics are given below:<br/><table class="wysiwyg-table"><tbody><tr><td>Physics</td><td>$48$</td><td>$60$</td><td>$72$</td><td>$62$</td><td>$56$</td><td>$40$</td><td>$39$</td><td>$52$</td><td>$30$</td></tr><tr><td>Mathematics</td><td>$62$</td><td>$78$</td><td>$65$</td><td>$70$</td><td>$38$</td><td>$54$</td><td>$60$</td><td>$32$</td><td>$31$</td></tr></tbody></table>Interpret the result.
Question 33 : The marks obtained by the students in physics and in mathematics are as follows.<br><table class="wysiwyg-table"><tbody><tr><td>Marks in Physics</td><td>35</td><td>23</td><td>47</td><td>17</td><td>10</td><td>43</td><td>9</td><td>6</td><td>28</td></tr><tr><td>Marks in Mathematics</td><td>30</td><td>33</td><td>45</td><td>23</td><td>8</td><td>49</td><td>12</td><td>4</td><td>31</td></tr></tbody></table>Compute of correlation of ranks.
Question 34 : In a skating competition the judges gave the five competitors the following marks. Calculate a coefficient of rank correlation.<br/><table class="wysiwyg-table"><tbody><tr><td>Competitors</td><td>A</td><td>B</td><td>C</td><td>D</td><td>E</td></tr><tr><td>1st judge</td><td>5.7</td><td>5.8</td><td>5.9</td><td>5.6</td><td>5.5</td></tr><tr><td>2nd judge</td><td>5.6</td><td>5.7</td><td>6.0</td><td>5.5</td><td>5.8</td></tr></tbody></table>
Question 35 : Calculate the Pearson's Coefficient of correlation between X and Y.<br><table class="wysiwyg-table"><tbody><tr><td>X</td><td>35</td><td>34</td><td>40</td><td>43</td><td>56</td><td>20</td><td>38</td></tr><tr><td>Y</td><td>32</td><td>30</td><td>31</td><td>32</td><td>53</td><td>20</td><td>33</td></tr></tbody></table>
