A statistical analysis of Unleaded 91 price in New South Wales

The key aim is to carry out a statistical analysis of Unleaded 91 in New South Wales
as on July 31, 2018 using selected descriptive statistics technique which aim at summarising
the sample values of price. The prices are quantitative in nature and the frequency histogram
of this variable is indicated below.
A key conclusion from the histogram indicated above is that the distribution of
Unleaded 91 price is asymmetric which hints at skew being present. Further, the given
distribution does not resemble a bell curve owing to the lowest class having the highest
frequency. Considering the evidence at hand, it may be appropriate to conclude that the
Unleaded 91 prices as on July 31, 2018 for NSW do not appear to be normally distributed.
On account of presence of skew, the measures of central tendency and dispersion need to be
adjusted since certain measures are quite susceptible to extreme values.
The summary statistics for the Unleaded 91 price sample data have been computed
using aid of Excel and presented as follows.

The skew in the given data is negative but quite low in magnitude. Further, the
average Unleaded 91 price for NSW as on July 31, 2018 stands at 143.51 cents per litre. This
is marginally lower than the corresponding median price of 144.30 cents per litre which
represents the price which is not exceeded by 50% of the sample observations considered.
With regards to dispersion, the standard deviation is 8.95 cents which is small considering the
value of mean price. The range of fuel price is also limited only and does not highlight huge
variation which is on expected lines. The IQR is 15.78 cents which is indicative of the fact
that the middle 50% data values of the sample tend to deviate in the narrow range of 15.78
cents per litre.