We measured the flat area of 30 apartments and we have measured the following values in \( m^{2} \) : \( 82.6,57.3,70.4,65,48.4,103.8,73.6,43.5,66.1,93,52.6,70,84.2,55,81.3,61.5,75.1,34.8 \), \( 62.4,116,70.1,63.6,93,59.2,65.9,77.2,52.8,68.7,79.2,87.4 \). a) Create a table of grouped frequency distribution for the number of classes \( k=9 \). b) Construct a histogram of relative frequencies of the flat areas. c) From the specified values estimate the sample mean and the variance. d) From the middle values of the intervals and from their frequencies estimate the sample mean and the variance.

Calculate the median in the given numbers below: \( 7,2,1,4,8,7,2,1 \)

Question 19. [ \( 5 \times 1 \) ] In sub part (i) and (ii) choose the correct option and sub-part (iii) to (v) answer the questions as instructed. (i) If the correlation coefficient between two variable is 1, then two least square lines of regression are: (a) parallel (b) perpendicular (c) coincident (d) both (a) and (c) (ii) Read the following statement and choose the correct option: (I) if \( b_{x y} \cdot b_{y x}=1 \), then the regression lines are perpendicular (II) If \( b_{x y} b_{y x}=0 \), then the regression lines are perpendicular (III) If \( b_{x y}+b_{y x}=0 \), then the regression lines are perpendicular (IV) \( \quad b_{x y}+b_{y x}=1 \), then the regression lines are perpendicular Which of the following is correct? (a) Only (II) is correct (b) Only (II) and (III) are correct (c) Only (I) and (IV) are correct (d) Only (I) is correct (iii) If the two line of regression are \( 3 x-2 y+1=0 \) and \( 2 x-y-2=0 \), then find the mean of \( x \) and mean of \( y \). (iv) A teacher asked his student to find the value of coefficient of correlation where two coefficient of regression are -0.3 and -1.2 . Fahad said the value of coefficient of correlation is \( \pm 0.6 \) Janhavi said the value of coefficient of correlation is - 0.6 How is correct? Justify your answer. (v) Find the value of \( b_{x y} \) for five observations of pairs( \( \left.\mathrm{x}, \mathrm{y}\right) \sum x=15, \sum y=25, \sum y^{2}= \) 135 and \( \sum x y=83 \). Question 19. [2] The equation of two line of regression are \( 2 x+3 y-6=0 \) and \( 5 x+7 y-12=0 \). Find the value of coefficient of correlation. Question 20. [4] The following observations are given: \[ (1,4),(2,8),(3,2)(4,12)(5,10),(6,14),(7,16)(8,6),(9,18) \] Estimate the value of \( y \) when the value of \( x \) is 10 Question 21. [4] The coefficient of correlation between the value denoted by \( X \) and \( Y \) is 0.5 . The mean of \( X \) is 3 and that of \( Y \) is 5 . Their standard deviation is 5 and 4 respectively. Find (i) The two line of regression (ii) The expected value of \( X \), when \( Y \) is given 9.

If a scatter plot shows points that are closely clustered together, what can you infer about the correlation between the variables?

Calculate the mode of this given data \( 2,3,2,1,4,4,1,1,3,2,5,3,5,1,5,1,4 \), \( 2,3,0,4,1,0,3,5,2,5,0,4,1,4,0,5,2,3,0,4,1,2 \)

1- Put the ( \( \vee \) ) mark against the statement if it is true and \( (x) \) if it false (10 POIN 1) The number of chlldren in a family is a qualitative data. 2) the mode is always found 3) For any two events \( A \) and \( B \) we must have \( P(A \cup B)=P(A)+P(B) \) 4) The sum of relative frequencies is 1 5) If the events \( A \& B \) are independent then \( \bar{A} \& \bar{B} \) are dependent 6) If the mean >median \( > \) mod the curve is skew from right. 7) The number of different permutations of word \( M I S S I S S I P P I \) is 3400 8) If the mode \( =24 \) and mean \( =60 \) then median \( =50 \). 9) In combination order is not important. 10) If \( X \) is a continuous random variable, then \( P(X=5)=0 \)