Statistical Analysis of Sales Data

This assignment presents a statistical analysis of sales orders, comparing sales between air and truck shipments using an independent sample t-test. It further explores the relationship between order quantity and sales revenue through correlation and regression analysis. The results are summarized in tables showcasing descriptive statistics, t-statistics, p-values, ANOVA findings, and regression coefficients, providing insights into the factors influencing sales performance.

Running head: FINANCE
Finance
Name of the student
Name of the university
Author’s note

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Executive Statistics
The sales data provided by Office sales pty Ltd is analysed herein. The analysis shows
that the sales data have four different priority levels, three shipping modes and four different
consumer segments. The analysis of the sample data shows that the maximum number of orders
have a critical priority. We find that most of the items are shipped thour regular air and most of
the items are sent by corporate customers. Moreover most of the items are shipped in two days.
The company gives priority to critical items for shipment. The analysis shows that the bulk of the
sales is for shippment through truck mode. In addition the relation between order quanity and
sales is poor.

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Table of Contents
Introduction......................................................................................................................................3
Analysis...........................................................................................................................................3
Descriptive Statistics....................................................................................................................3
Confidence Interval......................................................................................................................4
Hypothesis Testing.......................................................................................................................5
Correlation and Regression..........................................................................................................5
Conclusion and Limitations.............................................................................................................7
Appendices......................................................................................................................................8
Descriptive Statistics....................................................................................................................8
Confidence Interval....................................................................................................................13
Hypothesis Testing.....................................................................................................................14
Correlation and Regression........................................................................................................15

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Introduction
In this assignment we analyse the data of sales of banking. The data has been collected by
“Office Supplies Pty Ltd”. The company “Office Supplies Pty Ltd” provided the data pertaining
to 2000 orders. For the assignment 60 randomly selected orders were and analysed. There are
seven different variables whose information was provided by the organization. The variable
order is contains information of the identity of the order. The data also contains information
about the priority of the order, the mode of delivery, the customer type. Further information was
also provided about the number of days required to ship the order. The sales data analyses factors
which influences the sales of the company. Investigation is also done to check for differences in
shipping days based on order priority. We also investigate the relation between average sales ($)
value and order quantity.
Analysis
Descriptive Statistics
Order ID
The variable Order ID is used to track the order of the sales. This is an identity variable.
Order Priority
The data for order priority is presented in table 1 (appendix). Critical orders have the
highest frequency count of 18. The lowest frequency count is not specified order category. There
are 9 not specified orders in the sample data.
Order Quantity
The data for order quanity is presented in table 2 (appendix). The mean and median order
quantity is 26.15. The histogram for order quantity is presented in figure 3 (appendix). From the
histogram it can be said that the data for order quantity is evenly distributed. The spread of order
(coefficient of variation) is 55%.

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Sales
The data for sales is presented in table 3 (appendix). The mean sales value is $1895.331.
The median sales value is $500.045. Since the mean is more than the median sales value hence
data is skewed to the left. This is also depicted in the histogram for sales value (figure 4). The
spread of sales value (coefficient of variation) is 170%.
Ship Mode
The data for sales is presented in table 4 (appendix). The sample data shows that highest
number of orders are sent through regular air. The number of orders sent through regular air is
42. The least number of orders (8) are sent through express air.
Consumer Segment
The data for consumer segment is presented in table 5 (appendix). The analysis of the
data shows that Corporate customers have placed the maximum number of orders (24). The least
number of orders have been placed by cosnumers (11).
Days to Ship
The data for days to ship is presented in table 6 (appendix). The analysis of the data
shows that most of the orders (20) should be shipped in 2 days.
Confidence Interval
Confidence Interval 1
We are 95% confident that the average corporates sales lies within the limits 425.6539
and 2126.221. The mean sales for corporate consumers is $1275.937. The 95% confidence
interval would mean that if we take a second random sample of 60 orders then the average sales
to corporate consumers would lie within the limits 425.6539 and 2126.221 (table 7).
The mean sales for the population is $1,927.42 (table 9). Hence it is seen that the mean
sales for the population lies within the confidence interval for the sample data of corporate
customers.

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Confidence Interval 2
We are 95% confident that the average sales lies within the limits 1078.824 and
2711.837. The mean sales for all 60 orders is $1895.331. The 95% confidence interval would
mean that if we take a second random sample of 60 orders then the average sales would lie
within 1078.824 and 2711.837 (table 8).
The mean sales for the population is $1,927.42 (table 9). Hence it is seen that the mean
sales for the population lies within the confidence interval for the sample data.
Hypothesis Testing
Hypothesis 1
To test the hypothesis that the order priority “Critical” is shipped than the order priority
“Low” a two-tailed independent sample t-test is done. The test results are presented in table 10.
The test shows that 5% level of significance there is statistically significant differences between
avergae shipping days of Low and Critical, t(18) = -5.455, p-value <0.001.
The average number of days to ship low priority orders is 4.80 and the days to ship
Critical orders is 1.72.
Hypothesis 2
To test the hypothesis that the average sales for “Air” is different than “Truck” Delivery a
two-tailed independent sample t-test is done. The test results are presented in table 11. The test
shows that 5% level of significance there is statistically significant differences between avergae
Sales of Air and Truck, t(58) = -3.607, p-value = 0.001.
The average sales through Truck is $5155.66 and the average sales through Air is
$1319.98

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Correlation and Regression
Correlation
The relation between Order quantity and sales ($) is presented in Figure 1.
0 10 20 30 40 50 60
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
R² = 0.0496835106874372f(x) = 49.4562683107621 x + 584.739664764805
Relation of Sales ($) and Order
Quantity
Order Quantity
Sales ($)
Figure 1: Relation between Order quantity and sales ($)
The above presents the relation between order quantity and sales ($). The relation
between the two variables is represented through R2 = 0.0497 (table 12). Hence, 4.97% of the
variability of sales can be predicted with the order quantity. R2 is also known as the coefficient
of determination.
The correlation between the two variables is (Multiple R) 0.223. Thus the correlation is
weak, positive and linear.
The value of the sales cane be predicted through the equation (table 14):
 Sales ($) = 584.740 + 49.456*Order Quantity.
The ANOVA test is presented in table 13. For the variables F(1,58) = 3.032, p-value = 0.087.
Thus at 5% level of significance there is no relationship between order quantity and sales.

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The coeffecient of the slope is given as 49.456. Hence, we can say that for unit increase
in order quantity sales would increase by $49.456.
Conclusion and Limitations
The analysis of the data shows that the highest number of orders received by the
company have a critical priority. In addition Regular air shipment mode is the most preferred
mode of shipping the orders by the customers. Further the corporate houses provide the
maximum number of orders. It is also seen that most of the orders are shipped in two days. The
analysis of the data also shows that critical orders are shipped earlier than low priority orders.
Further the investigation also shows that the sales ($). The sales volume through truck delivery is
higher as compared to air delivery. Moreover it is seen that there is a weak relation between
order quantity and sales volume.
We have analysed the sales data for the organisation using a sample of 60 orders. The
limitation of the present analysis is the small sample size. We need to repeat the analysis by
taking more samples and analysing the data.

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Appendices
Descriptive Statistics
Order Priority
Table 1: Frequency of Order Priority
Order Priority Importance of Order Count
0 Not Specified 9
1 Low 10
2 Medium 13
3 High 10
4 Critical 18
Not Specified Low Medium High Critical
0
2
4
6
8
10
12
14
16
18
20
9 10 13 10 18
Importance of Order
Importance of Order
Frequency
Figure 2: Frequency of Order Priority

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Order Quantity
Table 2: Descriptive Statistics for Order Quantity
Descriptive Statistics Order Quantity
Mean 26.5
Median 26.5
Mode 15
Standard Deviation 14.54333
Range 49
Coefficient of Variation 55%
IQR 23.25
8 15 22 29 36 43 50
0
2
4
6
8
10
12
Histogram of Order Quantity
Order Quantity
Frequency
Figure 3: Histogram of Order Quantity

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Sales
Table 3: Descriptive Statistics for Sales
Descriptive Statistics Sales
Mean 1895.331
Median 500.045
Mode #N/A
Standard Deviation 3226.852
Range 16938.28
Coefficient of Variation 170%
IQR 2039.756
3000 6000 9000 12000 15000 18000
0
10
20
30
40
50
60
Histogram of Sales
Sales ($)
Frequency
Figure 4: Histogram of Sales
Ship Mode
Table 4: Frequency distribution of Ship Mode
Ship Mode Shipping Mode Count
1 Regular Air 43
2 Delivery Truck 9
3 Express Air 8

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Regular Air
72%
Delivery Truck
15%
Express Air
13%
Ship Mode
Figure 5: Distribution of Ship Mode
Consumer Segment
Table 5: Distribution of Consumer Segment
Consumer Segment Frequency
Corporate 24
Home Office 12
Consumer 11
Small Business 13

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Corporate Home Office Consumer Small Business
0
5
10
15
20
25
30
Distribution of Consumer Segment
Consumer Segment
Frequency
Figure 6: Distribution of Consumer Segment
Days to Ship
Table 6: Distribution of Days to Ship
Days to Ship Frequency
0 7
1 17
2 20
3 7
4 3
5 3
6 0
7 3

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0 1 2 3 4 5 6 7
0
5
10
15
20
25
Days to Ship
Days to Ship
Days
Figure 7: Days to Ship
Confidence Interval
Confidence Interval 1
Table 7: Confidence Interval of Corporate Customers
Statistics Value
Mean 1275.937
Standard Deviation 2125.266
Number 24
Standard Error 433.818
z-value 1.96
Margin of Error 850.2834
Lower Limit 425.6539
Upper Limit 2126.221

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Confidence Interval 2
Table 8: Confidence Interval for Sales
Statistics Value
Mean 1895.331
Standard Deviation 3226.852
Number 60
Standard Error 416.5848
z-value 1.96
Margin of Error 816.5063
Lower Limit 1078.824
Upper Limit 2711.837
Table 9: Average Sales for Population
Statistics Value
Mean 1927.42
Hypothesis Testing
Hypothesis Testing 1
Table 10: Independent Sample t-test for Critical and Low priority orders
Critical Low
Mean 1.72 4.80
Variance 0.80 4.40
Observations 18 10
Pooled Variance 2.047
Hypothesized Mean Difference 0
df 26
t Stat -5.455
P(T<=t) one-tail 0.000
t Critical one-tail 1.706
P(T<=t) two-tail 0.000
t Critical two-tail 2.056

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Hypothesis Testing 2
Table 11: Independent Sample t-test for Sales Orders by Truck and Air
Air Truck
Mean 1319.98 5155.66
Variance 7946940.17 13055549.43
Observations 51 9
Pooled Variance 8651575.930
Hypothesized Mean Difference 0
df 58
t Stat -3.607
P(T<=t) one-tail 0.000
t Critical one-tail 1.672
P(T<=t) two-tail 0.001
t Critical two-tail 2.002
Correlation and Regression
Table 12: Regression Statistics
Multiple R 0.223
R Square 0.050
Adjusted R Square 0.033
Standard Error 3172.672
Observations 60
Table 13: ANOVA
df SS MS F Significance F
Regression 1 30522667 30522667 3.032 0.087
Residual 58 5.84E+08 10065850
Total 59 6.14E+08
Table 14: Regression coefficient
Coefficients
Standard
Error t Stat P-value
Intercept 584.740 856.864 0.682 0.498
Order Quantity 49.456 28.401 1.741 0.087