MAT10251 Project: Descriptive Statistics of Fuel Prices in Queensland

This project presents a statistical analysis of Unleaded 91 fuel prices in Queensland on September 11, 2018, utilizing descriptive statistics. The analysis reveals a negatively skewed distribution, indicating that the mean price is influenced by lower extreme values. The mean Unleaded 91 price is 157.64 cents per litre, while the median is slightly higher at 158.90 cents per litre, which is considered a more appropriate measure of central tendency due to the data's skewness. The dispersion in fuel prices is relatively low, with a standard deviation of 5.40 cents. The Interquartile Range (IQR) of 8.10 cents per litre, which is a better measure of dispersion given the skewness, indicates that the central 50% of prices lie within this range. Prices ranged from 141.90 to 167.90 cents per litre. This analysis provides a comprehensive understanding of the fuel price distribution, highlighting key statistical measures and their interpretations.

The given statistical analysis using descriptive statistics tools aims at presenting a
summary of Unleaded 91 price in Queensland as on September 11, 2018. The relevant
frequency histogram for the Unleaded 91 price is highlighted as follows.
The histogram above clearly highlights that the shape of the fuel price distribution is
non-symmetric which is on account of skew being present in the data. In the given case, the
tail on the left side of the mean is longer than the corresponding tail on the right side, hence,
negative skew or leftward skew is present in the sample data. Thus, it may be correct to draw
conclusion about the non-normal nature of Unleaded 91 distribution for Queensland on
September 11, 2018. The skew present in this data would lead to some changes in the
appropriate measure for both dispersion and central tendency as some measures are more
susceptible to being influenced by extreme values than others.
For the sample data comprising of Unleaded 91 price for Queensland, the summary
statistics has been calculated using Excel and the result thus obtained is illustrated below.

It is apparent from the above summary statistics that the mean price on September 11.
2018 for Unleaded 91 price in QLD is 157.64 cents per litre. The median amount for the
same is little higher at 158.90 cents per litre. For the given dataset, the median would be the
appropriate indicator of central tendency since significant negative skew is present which
tends to distort the mean to a lower value. The dispersion in the Unleaded 91 prices is on the
lower end which is expected from fuel prices. While standard deviation is 5.40 cents but a
more accurate representation of dispersion is through IQR(Inter-Quartile Range) since skew
is present. The IQR for the data is 8.10 cents per litre which implies that the central 50%
values of Unleaded 91 lie within 8.10 cents only. Also, Unleaded 91 price in Queensland on
September 11, 2018 varies between 141.90 cents per litre to 167.90 cents per litre.
.