Statistics For Business And Finance

STATISTICS FOR
BUSINESS AND
FINANCE
STUDENT ID:
[Pick the date]

TASK 1
Part A
In order to draw out the given sample of 250 observations, the appropriate sampling
technique used is simple random sampling. One key feature of this sampling method is that
each element included in the population has equal probability of selection. But, there is a key
shortcoming of this sampling technique which is that the the various population attributes of
the population may not be faithfully captured when selecting sample. The key reason behind
this is that while undertaking random selection, the attributes of the population are not
considered (Medhi, 2016).
As a result, a better alternative is to switch to stratified random sampling. A key feature of
this is that the sample selected using this method would result in a more accurate
representation from the population. This would be the case since stratified sampling method
involves two steps. The first step is that the available population is divided based on its key
attributes i.e. those attributes which are relevant to the given study. From these sub-divided
population, sample is selected based on random sampling. However, care is taken so as to
draw only those many subjects from each group so that the proportion of the underlying
attribute in the sample is similar to that in population (Liebermann et al., 2015).
Part B
The numerical summary is represented below.
The box-whisker plot for the selected variables (Alcohol, Meals, Fuel and Phone) is given
below.
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Part C
The first key observation which may be derived from the above boxplots is that there is a host
of outliers in each of the foru variables. These would imply presence of a positive skew
whereby the tail to the mean right would be longer than the tail to the mean left. Since a
normal distribution is required to have a skew value of zero, hence the given variables would
not be normally distributed. Support for this conclusion can be derived based on descriptive
statistics where the skew values are quite high and also there is significant difference in mean
and median for the various variables. Further, the presence of outliers indicates that the
sample data contains certain individuals which tend to spend a disproportionately high
amount of either of the four categories of expenditure. In wake of the skew present, it would
be advisable that the central tendency for these variables be represented using median while
the dispersion is captured through Inter-quartile range. Traditional measures such as mean
and variance would be influenced by extreme values. The computation of median and IQR is
not influenced by the presence of extreme values and hence these are appropriate choices
(Eriksson and Kovalainen, 2015).
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