Answer to Question #182005 in Statistics and Probability for Andrew-John Bock

Question

QUESTION 1 [25 MARKS] The age distribution of guards hired by the Jumbo Department within the last year is: Age Number 20-29 2 30-39 13 40-49 20 50-59 12 60-69 3 a) Determine the class boundaries of the distribution. (3 marks) b) Construct a histogram and polygon of these data. (3 +3 marks) c) Construct a ‘less-than’ and ‘more-than’ cumulative frequency distribution. (2 +2 marks) d) Draw the ogives. (3 +3 marks) e) Based on the graph, the age of about half the guards hired was less than ….. (3 marks) f) Based on the graph, the age of about 30 of the guards hired was more than ….. (3 marks]

Answer 1

Solution:

(a):

Class Class boundaries: Frequency

20-29 19.5-29.5 2

30-39 29.5-39.5 13

40-49 39.5-49.5 20

50-59 49.5-59.5 12

60-69 59.5-69.5 3

(b): Histogram:

Frequency polygon:

(c):

Less than type cumulative table:

More than type cumulative table:

(d):

Less than type ogive:

More than type ogive:

(e): Based on the more than ogive graph in part (d), the age of about half the guards (i.e. 50/2=25) hired was less than 45 as it is (45,25)

(f): Based on the more than ogive graph in part (d), the age of about 30 of the guards hired was more than 42 as it is (42, 30).