MATH2123 – Problem Solving Task –
Abstract
The purpose of this report is to investigate whether there’s a significant difference in prices
between major supermarkets, Coles and Woolworths. The randomised of 50 matched items will be
responded to the tests where the units of price and weight are set in Australian dollars ($AU) and
kilogram or litre (kg/l), respectively. Furthermore, the construction of a 95% confident interval
(a=0.05) is assumed whereby limited the standard errors (SE) to be approximately 5%. Throughout the
analysis, graphs and plots will be used to highlight dataset and summarise overall statistics. Likewise,
hypothesis tests and p value are conducted to clarify the findings, and conclude whether there is a
sufficient relation between two variables or not.
SECTION 1
Average Coles Prices
The mean of Coles price is located
around 7.56. The shape of the data is
positively skewed and the spread of
the data is 40.1 meaning that values
are range from 1.9 to 42 with 5.35
median. The standard deviation of
7.08 shows that most of the data are
close to the average.
Average Woolworths Prices
The mean of Woolworths price is
located at 7.90 with the standard
deviation of 7.11. This indicates that
data are close to the average. The
shape of the data is positively skewed
and the spread is range from 1.4 to 42
suggested the median is around 5.
, Average Weights
The mean of 0.57 is close to a median
0.5, proving the shape of histogram is
symmetrical skewed and normally
distributed as the standard deviation
of 0.36 is close to the mean. The
range is located at 1.245 with the min
of 0.005 and 1.25 for the max.
Coles versus Woolworths
Coles
IQR = 5.39
Upper: 17.09 / Lower: -4.48
Woolworths
IQR = 5.5
Upper: 17.75 / Lower: -4.25
The box plots above display that Woolworths has more variable distribution with higher value of
standard deviation, 7.11. Despite, Coles is higher in range and median but when interpreting its
average price and the sum of total amount, it is significantly cheaper overall compared to Woolworths
with the values of mean 7.56 and $378.05 to 7.90 and $395.2.
Abstract
The purpose of this report is to investigate whether there’s a significant difference in prices
between major supermarkets, Coles and Woolworths. The randomised of 50 matched items will be
responded to the tests where the units of price and weight are set in Australian dollars ($AU) and
kilogram or litre (kg/l), respectively. Furthermore, the construction of a 95% confident interval
(a=0.05) is assumed whereby limited the standard errors (SE) to be approximately 5%. Throughout the
analysis, graphs and plots will be used to highlight dataset and summarise overall statistics. Likewise,
hypothesis tests and p value are conducted to clarify the findings, and conclude whether there is a
sufficient relation between two variables or not.
SECTION 1
Average Coles Prices
The mean of Coles price is located
around 7.56. The shape of the data is
positively skewed and the spread of
the data is 40.1 meaning that values
are range from 1.9 to 42 with 5.35
median. The standard deviation of
7.08 shows that most of the data are
close to the average.
Average Woolworths Prices
The mean of Woolworths price is
located at 7.90 with the standard
deviation of 7.11. This indicates that
data are close to the average. The
shape of the data is positively skewed
and the spread is range from 1.4 to 42
suggested the median is around 5.
, Average Weights
The mean of 0.57 is close to a median
0.5, proving the shape of histogram is
symmetrical skewed and normally
distributed as the standard deviation
of 0.36 is close to the mean. The
range is located at 1.245 with the min
of 0.005 and 1.25 for the max.
Coles versus Woolworths
Coles
IQR = 5.39
Upper: 17.09 / Lower: -4.48
Woolworths
IQR = 5.5
Upper: 17.75 / Lower: -4.25
The box plots above display that Woolworths has more variable distribution with higher value of
standard deviation, 7.11. Despite, Coles is higher in range and median but when interpreting its
average price and the sum of total amount, it is significantly cheaper overall compared to Woolworths
with the values of mean 7.56 and $378.05 to 7.90 and $395.2.
