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

Cite as características que um bom diagrama de dispersão deve ter para facilitar a interpretação dos dados.

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.

Bring out the median in this set of values: \( 1,2,2,4,8,9,3 \)

1. There are 330 workers in a factory. Out of them, 100 are females, 10 are literate and 100 are married. Moreover, 10 females are literate an married, 20 females are literate and unmarried, 25 married females ar illiterate and 5 "married and literates are males. By drawing the necessar venn-diagram, you are required to find: \( \begin{array}{ll}\text { i. No. of femaleworkers who are illiterate and unmarried. } \\ \text { ii. } \quad \text { No. of literate workers. who are unmarried males. } \\ \text { iii. } \quad \text { No. of married workers who are illiterate males. } \\ \text { iv. } \quad \text { No. of illiterate and unimarried male workers. }\end{array} \)