Answer to Question #152011 in Statistics and Probability for Astha Shukla

Question

52 33 70 95 57 61

57 64 54 94 38 61

50 39 94 63 59 31

68 88 93 48 82 82

74 70 92 76 98 91

32 33 31 75 54 48

36 64 63 66 92 98

36 54 71 86 84 55

91 34 64 67 89 78

97 92 53 56 68 55

93 42 51 77 36 93

44 66 63 33 68 79

83 53 86 76 35 40

55 41 36 39 42 96

60 53 38 51 95 56

48 69 49 33 95 37

83 62 96 34 85 32

39 59 77 62 35 34

54 89 36 45 83 34

39 61 88 86 55 33

69 54 30 38 79 77

95 34 38 91 80 90

88 45 95 71 80 43

61 40 31 61 58 53

91 63 60 94 98 53

50 34 75 74 90 98

1. Make the frequency distribution table with appropiate class interval, frequency,

cumulative frequency.

2. Calculate the standard deviation, variance and range

3. Make the following diagrams: Histogram, Frequency Polygon, Ogive

Answer 1

1) Frequency distribution table

2)

$variance = \frac{1}{N}\sum f_ix_i^2-\bar x^2$

$\bar x = mean = \frac{\sum f_ix_i}{\sum f_i}$

where f_i is frequency and x_i midpoint

$\bar x=\frac{9862}{156}=63.22$

$variance = \frac{1}{156}\cdot693399-63.22^2=448.10$

$\sigma=\sqrt{variance}=\sqrt{448.10}=21.17$

range = max value – min value = 98 – 30 = 68

3)