QUESTION ONE [35]
The following table represents the average weekly amount (rand) received from the private sector by registered South African charity organisations

 Amount Number of organisations 250 under 500 2 500 under 750 3 750 under 1 000 3 1 000 under 1 250 7 1 250 under 1 500 12 1 500 under 2 000 19 2 000 under 3 000 9 3 000 under 4 000 2 4 000 under 5000 1 5 000 under 10 000 8

Using the above grouped frequency distribution, construct an less than (upward sloping) ogive and estimate the value of the median using the graph. (8)
For the grouped frequency distribution above, use appropriate computational each of the:
the average weekly amount received from the private sector (3)
the modal weekly amount received from the private sector (3)
the median (4)
the 45th percentile. (4)
Calculate the coefficient of variation and comment on the value obtained (10)
From the measure of central tendency calculated in question 1.2 above comment on the skewedness of the data (3)

QUESTION TWO [20]

In an article published in the Sunday times it was reported that form companies that 25% of chief information officers (CIOs) report to the chief financial officers(CFO), 46% report to the chief executive officer (CEO) and the reminder report to someone other than CFO or CEO.
Suppose that 2 CIOs are selected at random form2 independent companies. Find the probability that:

• both report to the CEO (3)
• both report to someone other than the CFO or CEO (3)
• one reports to CFO and one reports to someone other than the CFO or CEO (4)
• at least one reports to the CEO. (4)

The Venn diagram below represents the following data. A = the number of households that have a notebook computer B = the number of households that have a smartphone
C = the number of households that have a tablet either a notebook computer or a tablet. (3)

QUESTION THREE [25]

A truck company decided to try to predict the fuel consumption for their long-distance hauls. They recorded the information below:

 Distance travelled (km) Amount of fuel used (L) 562 346 1894 1105 872 653 639 480 1405 950 1863 1200 786 563 462 340 356 220

Identify the depend on and the independent variable. (2)
Draw a scatter diagram of the data. (4)
Find the least square regression equation. (7) 3.4
data. (9)
3.5 Predict the amount of fuel for a truck that is about to travel 1450 km. (3)

QUESTION FOUR [20]
The average prices of a Bath & Shower gel, a Body Moisturisers, a Deodorants and a Shaving cream were recorded in both 2011 and 2021 as below. (Prices are in R.)

 Bath &Shower gel BodyMoisturisers Deodorants Shavingcream 2011 Price (R) 17 7.3 5.5 15.8 Number sold (inmillions) 7.5 4.2 12.6 8.5 2021 Price (R) 23.7 12.5 8.7 22.9 Number sold (inmillions) 8.2 5.1 13.5 9.5

Find the Laspeyres price and quantity indices for 2021 using a base year of 2011 and interpret your answer (10)
Find the Paasche price and quantity indices for 2021 using a base year of 2011 and interpret your answer. (10)