Question

The following were the scores obtained by Form II students in a Mathematics 

49

63

59

58

44

49

51

62

37

30

49

45

52

50

42

54

32

57

41

42

56

44

46

63

44

40

50

46

53

48

37

46

53

68

66

58

36

40

56

37

66

43

40

43

51

59

42

52

46

57

 

 

 

 

 

 

 

 

 

Required

a)     Group the data into 7 classes and Make a grouped frequency distribution          

 b)      70^th percentile mark                                                                                       

 c)   Standard deviation                                                                                        

Comment on the distribution of marks       

Answer 1

Solution

ii). 70th percentile

$$L+ \big( {0.7N - cf \over f} \big) i$$

70th perecentile lies on the 48-53 class, i.e 0.7(50)=35

$$=47.5 + ({0.7(50)-23 \over 12})6$$

=53.5

iii). Standard deviation

$$sd= \sqrt{ \sum x^2f(x)-{{(\sum xf(x))^2 \over \sum f(x)}}\over \sum f(x) -1}$$

$$= \sqrt{124842.5 - {2459 ^2\over 50} \over 49} =8.9316$$

=8.9316