Answer to Question #265654 in Statistics and Probability for sumbal

Question

 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).

Answer 1

(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 ${\frac {482} {821}}*100\approx58.7$ %