95 Use Excel’s Data > Data Analysis > Descriptive Statistics option and, where

necessary, the function key QUARTILE to answer the following questions:

(a) Find the mean, median and modal water usage across the 30 households.

(b) Find the variance and standard deviation of water usage per household.

(c) Find the first and the third quartile of water usage amongst the 30 households.

(d) Interpret the findings from (a) to (c) for the municipal officer who conducted this survey.

(e) If there are 750 households in the Paarl suburb, what is the most likely total water usage (in kl) amongst all these households:

(i) in a month?

(ii) in a year?

22 X3.22 – veal dishes

The price of a veal cordon bleu meal (in rand) was taken from the menus of 28 Durban restaurants in a survey conducted by Lifestyle magazine into the cost of

‘dining out’. The prices are:

48 66 60 90 58 68 53 63 64 55 64 58 54 72

56 80 55 62 75 48 55 45 48 72 52 68 56 70

Use Excel’s Data > Data Analysis > Descriptive Statistics option and, where necessary, the function keys QUARTILE and PERCENTILE, to answer the following questions:

(a) Define the random variable and its data type.

(b) Find the mean and median price of a veal cordon bleu meal. Interpret each measure.

(c) Can you identify a modal price? Give its value and discuss its usefulness.

(d) Identify the value of the standard deviation of the price of veal cordon bleu.

(e) Compute the skewness coefficient. Does the data appear to be skewed? If so, why?

(f) Which central location measure would you choose to report in the article on

‘dining out’? Why?

(g) What is the least price that a patron to one of these restaurants would pay if they dined out at any one of the most expensive 25% of restaurants?

(h) The least expensive 25% of restaurants do not charge above what price for the veal cordon bleu meal?

(i) What is the least price to be paid for the most expensive 10% of veal cordon bleu meals?

23 X3.23 – fuel bills

The monthly fuel bills of a random sample of 75 Paarl motorists who commute to work daily by car were recorded in a recent survey.

(a) Use the Data > Data Analysis > Descriptive Statistics option in Excel to find the mean, median, variance, standard deviation and skewness coefficient of the monthly fuel bill of the sample of car commuters.

(b) Interpret the meaning of each descriptive statistic in (a).

(c) Is the data skewed? If so, in what direction? What would be the cause of skewness?

(d) Find the coefficient of variation for monthly fuel bills. Is the relative variability between the sampled motorists’ monthly fuel bills low?

(e) Use the Excel function key QUARTILE to find the lower and upper quartiles of monthly fuel bills of motorists. Interpret each quartile.

(f) Compile the five-number summary table for monthly fuel bills.

(g) Construct a box plot of monthly fuel bills.

(h) Describe the profile of the monthly fuel bills of Paarl motorists who use their cars to commute daily to work and back.

(i) Assume that the cost of fuel is R10 per litre and that there are 25 000 motorists who commute to work daily in Paarl by car. Estimate the most likely total amount of fuel used (in litres) by all car commuters in Paarl in a month.

24 X3.24 – service periods

The Association of Professional Engineers recently surveyed a sample of 100 of its members to identify their years of experience.

(a) Use Excel’s Data > Data Analysis > Descriptive Statistics option to find the mean, median, standard deviation and skewness measure of the years of experience for the sample of professional engineers.

(b) Interpret the meaning of each descriptive statistical measure in (a).

(c) Use Excel’s Data > Data Analysis > Histogram option to compute a frequency distribution and a histogram of the years of experience for the sample data.

(Hint: Use the bin range given in the database.)

(d) Compute an interval for the years of experience of professional engineers that covers one standard deviation either side of the sample mean.

What percentage of the sampled professional engineers does this represent?

(e) The Association of Professional Engineers would like to see a mix of

‘experience’ and ‘new blood’ amongst its members. Ideally they would like to have at least 20% of their members with less than three years of experience (i.e.

‘new blood’ members) and at least 20% of their members with more than 12 years of service (i.e. ‘experienced’ members). Based on the histogram and frequency distribution in (c), is this desired mix of experience being achieved? Comment.

25 X3.25 – dividend yields

A survey of 44 JSE-listed companies recorded their dividend yields (as a percentage) for last year as shown in the following table:

5.3 4.8 3.1 4.1 6.1 4.1 3.2 4.6 7.6 1.6

4.6 1.9 4.8 2.9 1.5 5.1 2.8 3.6 3.3 5.5

2.8 4.2 3.6 3.1 5.9 2.9 3.6 4.1 4.9 2.7

3.7 7.1 6.2 2.8 5.1 3.8 3.4 3.9 5.8 6.3

6.8 4.3 5.1 5.4

(a) Define the random variable and its data type.

(b) Use Excel’s Data > Data Analysis > Descriptive Statistics option to find the mean, median, mode, standard deviation and skewness measure of the dividend yields of the JSE-listed companies.

97 (c) Interpret the meaning of each descriptive statistical measure in (b).

(d) Which central location measure would you use to report on the dividend yields of companies? Why?

(e) Use Excel’s Data > Data Analysis > Histogram option to compute a numeric frequency distribution and a histogram of the dividend yields of the sampled JSE companies. (Hint: Use the bin range given in the database.)

(f) Use Excel’s function key operations (MIN, MAX, MEDIAN and QUARTILE) to compute the five-number summary table.

(g) Construct a box plot of the dividend yields of the JSE-listed companies and interpret the profile of the dividend yields declared by JSE companies last year.

(h) What was the minimum dividend yield declared by the top 10% of JSE companies? (Hint: Use the PERCENTILE function key.)

(i) What percentage of JSE companies did not declare more than a 3.5% dividend yield last year? (Hint: Compute the ogive to find the cumulative percentages.) 26 X3.26 – rosebuds

A commercial flower grower in Hazyview sells fresh-cut rosebuds to retailers in Johannesburg. The unit price per rosebud (in cents) varies according to supply and demand. The grower has recorded the unit selling price for 100 transactions over the past two months.

(a) Define the random variable and data type.

(b) Use Excel’s Data > Data Analysis > Descriptive Statistics option to find the mean, standard deviation, median and skewness coefficient descriptive measures of the unit selling price of rosebuds.

(c) Compute and interpret the coefficient of variation of the unit selling price of rosebuds.

(d) Use Excel’s function key QUARTILE to compute the upper and lower quartiles of the unit selling price of rosebuds.

(e) What the highest unit selling price for the cheapest 25% of transactions?

(f) What was the minimum unit selling price received for the highest priced 25%

of transactions?

(g) What was the lowest unit selling price received for the highest-valued 10% of transactions?

(h) What was the highest unit selling price received for the lowest-valued 10% of transactions? (Hint: For (g) and (h) use the Excel function key PERCENTILE.) (i) Construct the five-number summary table and draw a box plot. Interpret the

profile of the unit selling price of rosebuds for the flower grower.