The objective of the given task is to analyse the fuel price for the state of Queensland as on September 11, 2018. The focus in this regards would be the price of Unleaded 91 for which 80 sample data is available. Descriptive statistics is the tool of choice for conducting analysis on the given sample data and is aimed at deriving the summary of the sample data. The given sample has not been used for deriving any conclusions about the underlying population of interest. The given data comprises of quantitative data expressed in numerical terms.
The requisite graphical summary of the sample values of price of Unleaded 91 as on September 11, 2018 in Queensland is indicated below.
The first key observation from the above histogram is that the shape is not symmetric. The tail on the left hand tends to be greater than the tail on the right hand. This is true for asymmetric shapes as in case of symmetric shapes the length of tail on both sides of the mean tends to be equal. Considering the asymmetric shape, it is apparent that skew is present in the fuel price and hence the underlying distribution cannot be considered as normally distributed. Further, negative skew is present in the given data which implies that potential outliers on the lower end may be present. As a result, for the given data, the central tendency would be best measured through the use of median and not the mean since it can be impacted by extreme values, which is not the case with median. Further, for measurement of dispersion, inter-quartile range would be preferred ahead of standard deviation since the former is not impacted by extreme values which cannot be said about the latter.
The relevant summary statistics for the given data are summarised below.
The above summary statistics confirms the presence of negative skew as analysed from the histogram. The mean price of Unleaded 91 has been computed as 157.64 cents per litre. The median price is slightly higher at 158. 90 cents per litre and is more representative owing to the presence of skew. The dispersion in the data is quite small which is apparent from the various measures such as range, variance and standard deviation. However, the most suitable measure of dispersion for the given skewed data is inter-quartile range. The inter-quartile range is 8.10 cents which implies that the middle 50% of the fuel prices lie within this narrow range.
Based on the above analysis, it is apparent that the underlying sample fuel prices do not exhibit a normal distribution as negative skew is present. As a result, the central tendency is represented using median which has a value of 158.90 cents. Additionally, the dispersion in the fuel prices is best captured by the inter-quartile range which is quite small at 8.10 cents. It can be concluded that unleaded 91 prices have a small dispersion.