Question 1: 50 marksa)For both SAL04 and SAL 09 separately: i)Construct a histogram from the frequency information above. ii)Construct the cumulative frequency diagram, then use it to estimate the median, and the two quartiles Q1 and Q3 Using the cumulative frequency diagram following are the required statistics for the respective salary ranges: SAL04:Median17,750Q1 15,375 Q3 20,125 SAL09:Median27,500Q1 22,750 Q3 32,250 Using the frequency table, determine the mean, median, standard deviation and inter-quartile range for the salaries. Following are the required statistics using the frequency table: SAL04:Mean 17,750 Median18,000Std Dev 2,958 Inter quartile range 4,750 SAL09:Mean 27,500 Median 28,000 Std Dev 5,916 Inter quartile range 9,500 From the individuals’ data in the file Salary Survey. xls use Excel to evaluate the mean, median, standard deviation and inter-quartile range for the SAL04 and SAL09.We get the following values using Excel: SAL04SAL09Mean 17,904 34,539 Median18,007 23,625.82 Std Dev 949.9 28,961 Inter quartile range 4,750 5,335 c)The two curves can be shown appearing slowly along the line and then stabilizing.
During the initial stage, i.e. , at the time of graduation, the rate of salary growth is slow.
Rate of growth then increases rapidly 5 years after graduation. After some time the growth rate slows down. Question 214 marksA company has a large number of accountants. Records show that 30 are qualified to work with SMEs (small or medium sized enterprises), 25 are qualified to work with large international companies and 28 are qualified to work with Local Authorities. Of the accountants who can work with Local Authorities, 3 can work with international companies and SMEs, 5 can work with international companies but not with SMEs, 9 can work with SMEs but not international companies.
Of the accountants who can work with international companies, 6 can work with SMEs but not with Local AuthoritiesRepresent this information in a diagram (a Venn diagram would be suitable). P(LA)= 28P(LIC AND SME)lLA)=3P(LIC OR SHow many accountants took part in the survey? P(SME U LIC U LA) = 57 accountants took part in the survey If an accountant is chosen at random what is the probability that he/she can: Do all 3 types of work? P(all 3 types of work) = 34/57 = 0.59Do only one of the types of work? P (only one of the types of work) = 12/57 + 11/57 + 11/57 = 0.596 ~ 0.60If those accountants who are qualified to work with international companies are busy; what proportion of the remaining accountants are qualified to work with both SMEs and Local Authorities? 9/32 or 28% of the remaining accountants are qualified to work with both SMEs and Local Authorities What practical use could the company make of this information from these records?
(3 marks)This information would prove to be very useful for the company in the times to come.
This is because it would have a clear picture as to where could the accountants be placed as per their qualifications. Furthermore, it would also show the company management the area where more accountants are needed given the demand for certain requirements in the industry. Question 312 marksApplicants for a certain job are given an aptitude test. Past experience shows that the scores from the test are normally distributed with a mean of 60 and standard deviation of 12 marks. What percentage of applicants would be expected to pass the test if the minimum score required was 75?