Data Analysis and Decision Modelling Oz Assignments
Delivery in day(s): 4
Visual presentation of the prices based on product from different brands
Price of Calvin Klein  Price of Zara  Price of Tommy Hilfiger  Price of Ralph Lauren 
94.27  47.53  60.73  63.77 
70.71  48.87  87.92  97.55 
60.48  58.19  47.07  64.47 
61.83  32.64  96.78  149.02 
73.78  54.35  83.47  29.53 
82.79  51.75  92.30  95.28 
65.26  75.09  35.89  131.19 
48.48  61.67  118.92  54.59 
78.00  31.28  98.56  100.66 
81.44  42.92  72.89  111.94 
128.17  72.02  49.06  32.78 
31.00  28.04  14.38  80.25 
37.42  60.34  79.39  89.56 
64.86  59.32  130.20  115.84 
63.02  34.98  41.18  22.08 
84.65  56.49  47.57  38.35 
84.74  25.07  29.02  41.41 
86.82  36.22  44.24  62.18 
50.59  70.48  87.10  77.11 
41.17  39.91  60.49  45.88 
57.74  46.55  72.93  60.77 
29.09  48.50  98.93  41.05 
63.03  52.36  52.82  94.84 
60.27  66.86  123.02  89.81 
56.75  38.36  15.42  74.94 
44.24  51.88  56.38  73.80 
109.63  47.16  103.36  60.55 
101.15  54.65  105.25  44.30 
100.12  66.34  86.78  42.48 
75.55  73.45  124.03  59.07 
Charts
One of the fundamental aspects in representing the data output on prices is through distribution. The price distribution arises because the rates will not yield the same at every time due to various macro and micro economic factors. Therefore, there exist a scattering of values around central tendency. The location, shape and variability of the distributions can be analysed using the following tools. (Freedman, 2010)
Location – Mean & median; Spread – Variance, Standard deviation and range and Shape – Skewness and Kurtosis
The descriptive statistics of prices
 Calvin Klein 




Location  Mean  69.56889 
 Median  65.05888 
Spread  Standard Deviation  23.37837 
 Sample Variance  546.5483 
 Range  99.08802 
Shape  Kurtosis  0.111549 
 Skewness  0.401199 
 Minimum  29.08674 
 Maximum  128.1748 
 Count  30 
 Zara 




Location  Mean  51.10847 
 Median  51.8144 
Spread  Standard Deviation  13.86985 
 Sample Variance  192.3726 
 Range  50.02136 
Shape  Kurtosis  0.77666 
 Skewness  0.05338 
 Minimum  25.06978 
 Maximum  75.09114 
 Count  30 
 Tommy Hilfiger 




Location  Mean  73.86924 
 Median  76.16283 
Spread  Standard Deviation  32.29041 
 Sample Variance  1042.671 
 Range  115.8186 
Shape  Kurtosis  0.86718 
 Skewness  0.06482 
 Minimum  14.38371 
 Maximum  130.2023 
 Count  30 
 Ralph Lauren 




Location  Mean  71.50168 
 Median  64.12269 
Spread  Standard Deviation  31.26372 
 Sample Variance  977.4204 
 Range  126.9439 
Shape  Kurtosis  0.07787 
 Skewness  0.600018 
 Minimum  22.07529 
 Maximum  149.0192 
 Count  30 
From the above descriptive analysis it is noted that the mean and median value of Calvin Klein is different, the mean states the average of the distribution whereas the median states the 50 percentile of the data or the mid value. However, it is noted that mean and median of Zara is almost same at 51, however Tommy Hilfiger and Ralph Lauren is also have a difference between the mean and median
While measuring the spread of the data, the standard deviation of Calvin Klein, Tommy Hilfiger and Ralph Lauren has highest value, this shows that the deviation of the values from the mean is huge. Therefore a large standard deviation means the observed value has a huge difference when compared with mean. Therefore the goal should be less standard deviation which is noted in Zara. Therefore, it can be stated that the mean value of Zara has more meaningful information . (Triola, 2014)
In order to analyse the shape of the data, skewness and kurtosis is applied, skewness will state the symmetry of the data. A data to be normally distributed should possess the value of skewness as 0. Similarly Kurtosis is used to measure the combined size of two tails of information, for a data to be normally distributed should have value equal to 3. In the descriptive analysis it is noted that Zara and Tommy Hilfiger has a skewness value almost 0, whereas Calvin Klein and Ralph Lauren have values more than 0, therefore these two products are asymmetrical and the prices may not have normal distribution.
Visual representation
 Business Style 




Location  Mean  89.14395 
 Median  87.36749 
Spread  Standard Deviation  22.28638 
 Sample Variance  496.6829 
 Range  73.71693 
Shape  Kurtosis  0.94622 
 Skewness  0.274778 
 Minimum  56.48535 
 Maximum  130.2023 
 Count  30 
 Sports style 




Location  Mean  64.06367 
 Median  61.19693 
Spread  Standard Deviation  15.32209 
 Sample Variance  234.7665 
 Range  62.71523 
Shape  Kurtosis  0.6026 
 Skewness  0.34497 
 Minimum  36.21763 
 Maximum  98.93286 
 Count  30 
 Casual style 




Location  Mean  41.33898 
 Median  41.17424 
Spread  Standard Deviation  13.02517 
 Sample Variance  169.655 
 Range  50.87537 
Shape  Kurtosis  0.36824 
 Skewness  0.11966 
 Minimum  14.38371 
 Maximum  65.25908 
 Count  30 
From the above descriptive analysis it is noted that the mean and median value of Business style and Sports style wears are different, the mean states the average of the distribution whereas the median states the 50 percentile of the data or the mid value. However, it is noted that mean and median of Casual style wear is almost same at 41. Therefore the mean and median is closely related for Casual style wear. (Boslaugh, 2012)
While measuring the spread of the data, the standard deviation of Business style has highest value with 22.28, this shows that the deviation of the values from the mean is huge. Therefore a large standard deviation means the observed value has a huge difference when compared with mean. Therefore the goal should be less standard deviation which is noted in Sports style and Casual style with SD of 15.32 and 13.02 respectively. Therefore, it can be stated that the mean value of Business style and Casual style has more meaningful information .
In order to analyse the shape of the data, skewness and kurtosis is applied, skewness will state the symmetry of the data. A data to be normally distributed should possess the value of skewness as 0. Similarly Kurtosis is used to measure the combined size of two tails of information, for a data to be normally distributed should have value equal to 3. In the descriptive analysis it is noted that Casual style has a skewness value almost 0, whereas Business style and Sports style have values more than 0, therefore these two style are asymmetrical and the prices may not have normal distribution.
Zara business  Zara sports  Zara casual 
58.19  54.35  47.53 
75.09  51.75  48.87 
72.02  61.67  32.64 
60.34  42.92  31.28 
59.32  36.22  28.04 
56.49  48.50  34.98 
70.48  52.36  25.07 
66.86  51.88  39.91 
66.34  47.16  46.55 
73.45  54.65  38.36 
 Zara business style 




Location  Mean  65.85872 
 Median  66.60369 
Spread  Standard Deviation  6.859775 
 Sample Variance  47.05652 
 Range  18.60579 
Shape  Kurtosis  1.73364 
 Skewness  0.07044 
 Minimum  56.48535 
 Maximum  75.09114 
 Count  10 
 Zara sports style 




Location  Mean  50.14484 
 Median  51.8144 
Spread  Standard Deviation  6.984534 
 Sample Variance  48.78372 
 Range  25.45067 
Shape  Kurtosis  1.056389 
 Skewness  0.56811 
 Minimum  36.21763 
 Maximum  61.6683 
 Count  10 
 Zara casual style 




Location  Mean  37.32185 
 Median  36.6685 
Spread  Standard Deviation  8.370247 
 Sample Variance  70.06104 
 Range  23.8008 
Shape  Kurtosis  1.32792 
 Skewness  0.102239 
 Minimum  25.06978 
 Maximum  48.87058 
 Count  10 
From the above descriptive analysis it is noted that the mean and median value of all style of products of Zara looks same, the mean states the average of the distribution whereas the median states the 50 percentile of the data or the mid value. However, it is noted that mean and median of all products of Zara is almost same.
The goal should be less standard deviation which is noted in Business style, Sports style and Casual style of Zara products are less. Therefore, it can be stated that the mean value of all products are closely related to the mean value.
In order to analyse the shape of the data, skewness and kurtosis is applied, skewness will state the symmetry of the data. A data to be normally distributed should possess the value of skewness as 0. Similarly Kurtosis is used to measure the combined size of two tails of information, for a data to be normally distributed should have value equal to 3. In the descriptive analysis it is noted that business style has a skewness value almost 0, whereas sports style and Sports style have values more than 0, therefore these two style are asymmetrical and the prices may not have normal distribution. (Witte, 2010)
A ttest is one of the statistical test which helps the researcher to determine whether the two set of data is significantly different from each other. A t test is one of the commonly implemented test analysis, which will follow the steps of the normal distribution. It should be noted that when the scaling term is unknown and it is replaced by an estimate which is available on the data then we can follow students ttest. (Sincich, 2012)
The first step is to formulate the hypothesis, the null hypothesis will state that there mean difference is the same or to put it in other words, there is no significant difference between the variables. The alternate hypothesis will be stated as there is a significant difference among the variables. The interpretation of the data can be stated if the test statistic value is greater than the significance value then null hypothesis is rejected and alternate hypothesis is accepted. (Freedman, 2010)
In the given problem, the objective is to test if there is a significant difference in average prices across these two gender targets. Therefore the following hypothesis is framed.
Null hypothesis: There is no significant difference between average prices and gender
Alternate hypothesis:There is a significant difference between average prices and gender
tTest: TwoSample Assuming Unequal Variances 







 Price  Gender 

Mean  66.51207  1.5 

Variance  754.4582  0.252101 

Observations  120  120 

Hypothesized Mean Difference  0 


df  119 


t Stat  25.92355 


P(T<=t) onetail  0.004 


t Critical onetail  1.657759 


P(T<=t) twotail  0.008 


t Critical twotail  1.9801 


From the above ttest analysis it can be noted that mean value of price is 66.51 and the gender is 1.5, the variance of prices are high when compared with the gender.
It is further noted that t statistic is 25.92 whereas the p value is 0.004, this shows that the mean of values between price changes and gender are same. Therefore, null hypothesis is accepted. Hence it is stated that there is no significant difference between average prices and gender.
A ttest is one of the statistical test which helps the researcher to determine whether the two set of data is significantly different from each other. A t test is one of the commonly implemented test analysis, which will follow the steps of the normal distribution. It should be noted that when the scaling term is unknown and it is replaced by an estimate which is available on the data then we can follow students ttest.
The first step is to formulate the hypothesis, the null hypothesis will state that there mean difference is the same or to put it in other words, there is no significant difference between the variables. The alternate hypothesis will be stated as there is a significant difference among the variables. The interpretation of the data can be stated if the test statistic value is greater than the significance value then null hypothesis is rejected and alternate hypothesis is accepted.
In the given problem, the objective is to test if there is a significant difference in average prices across brands. Therefore the following hypothesis is framed.
Null hypothesis:There is no significant difference between average prices and brands
Alternate hypothesis:There is a significant difference between average prices and brands
tTest: TwoSample Assuming Unequal Variances 





 Price  Brands 
Mean  66.27881803  2.512605042 
Variance  754.2678226  1.25195841 
Observations  119  119 
Hypothesized Mean Difference  0 

df  118 

t Stat  25.30703038 

P(T<=t) onetail  0.008 

t Critical onetail  1.657869523 

P(T<=t) twotail  0.001 

t Critical twotail  1.980272226 

From the above ttest analysis it can be noted that mean value of price is 66.27 and the brands is 1.5, the variance of prices are high when compared with the brands.
It is further noted that t statistic is 25.30 whereas the p value is 0.008, this shows that the mean of values between price changes and brands are same. Therefore, null hypothesis is accepted. Hence it is stated that there is no significant difference between average prices and brands.
A ttest is one of the statistical test which helps the researcher to determine whether the two set of data is significantly different from each other. A t test is one of the commonly implemented test analysis, which will follow the steps of the normal distribution. It should be noted that when the scaling term is unknown and it is replaced by an estimate which is available on the data then we can follow students ttest.
The first step is to formulate the hypothesis, the null hypothesis will state that there mean difference is the same or to put it in other words, there is no significant difference between the variables. The alternate hypothesis will be stated as there is a significant difference among the variables. The interpretation of the data can be stated if the test statistic value is greater than the significance value then null hypothesis is rejected and alternate hypothesis is accepted. (Freedman, 2010)
In the given problem, the objective is to test if there is a significant difference in average prices across styles. Therefore the following hypothesis is framed.
Null hypothesis: There is no significant difference between average prices and styles
Alternate hypothesis:There is a significant difference between average prices and styles
tTest: TwoSample Assuming Unequal Variances 





 Prices  Styles 
Mean  66.27881803  2.008403361 
Variance  754.2678226  0.66942031 
Observations  119  119 
Hypothesized Mean Difference  0 

df  118 

t Stat  25.51697319 

P(T<=t) onetail  0.003 

t Critical onetail  1.657869523 

P(T<=t) twotail  0.007 

t Critical twotail  1.980272226 

From the above ttest analysis it can be noted that mean value of price is 66.27 and the styles is 2.0, the variance of prices are high when compared with the styles.
It is further noted that t statistic is 25.5 whereas the p value is 0.003, this shows that the mean of values between price changes and styles are same. Therefore, null hypothesis is accepted. Hence it is stated that there is no significant difference between average prices and styles.
A ttest is one of the statistical test which helps the researcher to determine whether the two set of data is significantly different from each other. A t test is one of the commonly implemented test analysis, which will follow the steps of the normal distribution. It should be noted that when the scaling term is unknown and it is replaced by an estimate which is available on the data then we can follow students ttest.
The first step is to formulate the hypothesis, the null hypothesis will state that there mean difference is the same or to put it in other words, there is no significant difference between the variables. The alternate hypothesis will be stated as there is a significant difference among the variables. The interpretation of the data can be stated if the test statistic value is greater than the significance value then null hypothesis is rejected and alternate hypothesis is accepted.
In the given problem, the objective is to test if there is a significant difference in Zara average prices across Zara styles. Therefore the following hypothesis is framed.
Null hypothesis:There is no significant difference between Zara average prices and Zara styles
Alternate hypothesis:There is a significant difference between Zara average prices and Zara styles
Zara prices and styles can be grouped as follows
PRICE  STYLE 
47.53  3 
48.87  3 
58.19  1 
32.64  3 
54.35  2 
51.75  2 
75.09  1 
61.67  2 
31.28  3 
42.92  2 
72.02  1 
28.04  3 
60.34  1 
59.32  1 
34.98  3 
56.49  1 
25.07  3 
36.22  2 
70.48  1 
39.91  3 
46.55  3 
48.50  2 
52.36  2 
66.86  1 
38.36  3 
51.88  2 
47.16  2 
54.65  2 
66.34  1 
73.45  1 
tTest: TwoSample Assuming Unequal Variances 





 Zara prices  Zara styles 
Mean  51.23195651  1.965517241 
Variance  198.7692613  0.677339901 
Observations  29  29 
Hypothesized Mean Difference  0 

df  28 

t Stat  18.78610969 

P(T<=t) onetail  0.0014 

t Critical onetail  1.701130908 

P(T<=t) twotail  0.002 

t Critical twotail  2.048407115 

From the above ttest analysis it can be noted that mean value of Zara average price is 51.23 and the styles of Zara is 1.96, the variance of prices are high when compared with the styles.
It is further noted that t statistic is 18.8 whereas the p value is 0.001, this shows that the mean of values between price changes and styles are same. Therefore, null hypothesis is accepted. Hence it is stated that there is no significant difference between Zara average prices and Zara styles.
Boslaugh, Sarah (2012). Statistics in a Nutshell. Cengage Publishing
Freedman, David (2010). Statistics. 4th Edition. Cengage Publishing
Sincich, T. Terry (2012). Statistics. 12th Edition.
Triola (2014). Essentials of Statistics. 5th Edition. McGraw Hill
Witte, S. Robert. (2010). Statistics. 5th Edition. McGraw Hill