The table below shows the distribution of salaries of employees in Dun ford and Sons. SALARY RANGE & NO. OF EMPLOYEES
Salary range 5,000-9,999 10,000-14,999 15,000-19,999 20,000-24,999 25,000-29,999 30,000-34,999 35,000+
No. of Employees
56
134
292
149
127
38
25
a) Make the necessary calculations and draw a cumulative frequency.
b) Calculate the number of managers, given that senior managers’ salaries are £30,000 and above, and middle managers’ salaries are greater than £20,000.
c) Calculate the ratio of senior managers to middle managers.
d) Calculate the percentage of the workforce which are not senior or middle managers (i.e. other employees).
(a) Cumulative frequency represents the amount of observation that are smaller than a considered one
For the given data we have
CF(5000) = 0
CF(10000) = 0 + 56 = 56
CF(15000) = 56 + 134 = 190
CF(20000) = 190 + 292 = 482
CF(25000) = 482 + 149 = 631
CF(30000) = 631 + 127 = 758
CF(35000) = 758 + 38 = 796
CF("\\infty") = 796 + 25 = 821
(b) There are 821 - 758 = 63 senior managers and 758 - 482 = 276 middle managers
(c) "{\\frac {63} {276}}={\\frac {21} {92}}\\approx0.228"
(d) There are 821 - 276 - 63 = 482 other employees, which means they constitute "{\\frac {482} {821}}*100\\approx58.7" %
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