Answer to Question #272889 in Statistics and Probability for james

Question

The following are weights in kilograms of

40

students recorded.

90.0 119.0 97.5 78.3 76.5

86.5 109.3 102.3 89.6 79.0

65.7 87.5 95.6 85.3 96.5

70.3 75.7 83.5 75.6 107.3

49.8 56.3 69.5 86.5 63.2

53.7 75.8 68.3 63.2 68.9

53.7 75.8 68.2 80.6 81.3

54.0 110.5 86.2 80.6 81.3

45.6 100.2 75.6 51.2 93.0

(i) Determine the suitable size of class interval. [1 Mark]

(ii) Construct a frequency distribution table, show a column of tally, midpoints, lower

and upper boundary for each class. [6 Marks]

(iii) Construct a frequency polygon superimposed on a histogram and comment on the

weight of the students. [4 Marks]

(iv) Construct a cumulative frequency curve and use it to determine median weight.

[3 Marks]

(v) Determine the mean and standard deviation using the frequency distribution in (ii)

above. [6 Marks]

Answer 1

Least to Greatest Values:

45.6, 49.8, 51.2, 53.7, 53.7, 54, 56.3, 63.2, 63.2, 65.7, 68.2, 68.3, 68.9, 69.5, 70.3, 75.6, 75.6, 75.7, 75.8, 75.8, 76.5, 78.3, 79, 80.6, 80.6, 81.3, 81.3, 83.5, 85.3, 86.2, 86.5, 86.5, 87.5, 89.6, 90, 93, 95.6, 96.5, 97.5, 100.2, 102.3, 107.3, 109.3, 110.5, 119

i)

suitable size of class interval: 10

ii)

iii)

from histogram:

minimal frequency: classes 40-50 and 110-120

maximal frequency: class 80-90

iv)

from cumulative frequency curve:

median = 80

v)

mean:

$\mu=\frac{\sum x_i f_i}{n}=\frac{45\cdot2+55\cdot5+65\cdot7+45\cdot2+75\cdot9+85\cdot11+95\cdot5+105\cdot4+115\cdot2+}{45}=77.33$

standard deviation:

$\sigma=\sqrt{\frac{\sum x_if_-n\mu^2}{n-1}}=17.63$