Answer to Question #206720 in Statistics and Probability for Carmz

Question

The price (in rands) in June of a 1 kg packet of laundry in KwaDukuza is shown

is shown below for each 5 years.

Year 2016 2017 2018 2019 2020

Price 17.8 29.6 41.1 46.3 46.5

Find the percentage increase in the price of laundry detergent between each period.

Use the 4 percentages in question 2.2.1 above, to calculate the overall geometric

mean percentage increase in the price of laundry detergent each year.

Interpret the geometric mean calculated above

Answer 1

The percentage increase in the price:

2016-2017:

$\frac{29.6-17.8}{17.8}=66.3\ \%$

2017-2018:

$\frac{41.1-29.6}{29.6}=38.9\ \%$

2018-2019:

$\frac{46.3-41.1}{41.1}=12.7\ \%$

2019-2020:

$\frac{46.5-46.3}{46.3}=0.4\ \%$

Geometric Mean = [Product of (1 + R_n)]^1/n -1

where Rn = 0.04 is growth rate for year n

2016-2017, n=1:

$1+0.663-1=66.3\ \%$

2017-2018, n=2:

$\sqrt{(1+0.663)(1+0.389)}-1=52.0\ \%$

2018-2019, n=3:

$\sqrt[3]{(1+0.663)(1+0.389)(1+0.127)}-1=37.6\ \%$

2019-2020, n=4:

$\sqrt[4]{(1+0.663)(1+0.389)(1+0.127)(1+0.004)}-1=27.1\ \%$

Geometric mean gives more accurate value of increase in the price per year.