Answer to Question #221721 in Statistics and Probability for kitto

Question

11 8 15 12 11 12 11 14 15 5 6 11

16 14 13 14 13 9 11 19 12 10 13 5

13 7 3 14 13 16 20 15 5 15 15 5

15 7 9 11 17 18 10 14 9 7 4 15

13 12 16 8 12 12

Draw any one of the following graphs to represent the data

i.       Histogram

 ii.     Frequency polygon

iii.     Ogive

v.      Pie chart

vi.     Box-and-whisker plot

Briefly explain:

(i) Why you chose to use this type of graph; and                               

(ii) What it shows about the data and the data generating process.     

Answer 1

Solution:

Arranging given data in ascending order:

3, 4, 5, 5, 5, 5, 6, 7, 7, 7, 8, 8, 9, 9, 9, 10, 10, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 16, 16, 16, 17, 18, 19, 20.

(i) A histogram would be better here as this data has many observations with many frequencies.

(ii) Frequency polygon and Ogive can be formed using histogram, so they need further steps after histogram. Pie chart would require a lot of calculation to show data in degrees. Box-and-whisker plot is inappropriate as this data does not have any outliers.

Histogram shows all the observations with their present frequencies using bars which can be easily interpreted. Also, it shows that maximum observations lie in 11-15 interval and minimum lie in 19-23.