Question One
Avocados for export are graded according to their weights. They are graded as poor grade if their weight falls below 300 gms, good grade if between 300 gms and 400 gms, and average grade if above 400 gms. The following table shows the distribution of avocados supplied for export by one farmer
Weight (in gms) | Number of Avocados |
0 and less than 100 | 4 |
100 and less than 200 | 10 |
200 and less than 300 | X |
300 and less than 400 | Y |
400 and less than 500 | Z |
500 and less than 600 | 6 |
600 and less than 700 | 4 |
TOTAL | 230 |
The median and mode of the distribution of avocados supplied for export by the farmer is known to be 335 gms and 340 gms respectively.
Required:
a) Suppose the farmer receives Kshs 5 for each avocado graded as poor, Kshs 15 for
each good grade avocado, and Kshs 10 for each average one. How much is the farmer likely to take home for his supply?
b) Based on the distribution of avocado supplied by the farmer in a) compute:
(i) Mean gms
(ii) Standard deviation gms
(iii) Coefficient of skewness
c) Critically examine the different methods of measuring dispersion
(Total Mark allocation for Question One = 15 Marks)
Question Two
a) (I) A company wants to know the relationship between the size of its “sales force”
and its yearly “sales revenue”. Records for the first five years are as follows:
Year | 2015 | 2016 | 2017 | 2018 | 2019 |
No. of Sales Staff | 15 | 18 | 15 | 22 | 25 |
Revenue (Kshs ‘000) | 10.1 | 16.3 | 23.3 | 16.3 | 24.1 |
Required
Use the given data to determine;
(i) The product moment (Pearson’s) correlation coefficient
(ii) The rank (Spearman’s) correlation coefficient.
(iii) Interpret your results from (i) and (ii).
(II) Given that the company has sent out 30 sales staff to market the company’s products this year, determine the expected revenue.
b) You are a businessman who invests your come as it comes. Let X and Y be sets of the annual incomes and expenditure, respectively, for the last five years.
You have initially computed the following values from the data with the intention determining estimates for expenditure
, , , , ,
Required
You have just realized that in recording the data the values of and were wrongly recorded as 4 and 3, instead of 3 and 4. Make adjustments to each of the above five computations that you made in order to obtain the correct values of the computations.
(Total Mark allocation for Question Two = 15 Marks)