Financial Statistics for Desklib Online Library

This article discusses financial statistics including quantitative and qualitative variables, confidence intervals, hypothesis testing, and correlation and regression analysis. It provides detailed information on mean, median, mode, standard deviation, variance, minimum, maximum, range, coefficient of variation, 1st quartile, 3rd quartile, and inter quartile range. It also includes graphical representations of the data. The article is relevant for students studying finance and statistics in college or university.

Running head: FINANCIAL STATISTICS
Financial Statistics
Name of the Student:
Name of the University:
Author’s note:

1FINANCIAL STATISTICS
Table of Contents
Tasks..........................................................................................................................................3
Task 1:....................................................................................................................................3
Task 2:....................................................................................................................................3
Quantitative Variables:.......................................................................................................3
Qualitative Variables:.........................................................................................................5
Task 3 – Confidence Interval:................................................................................................9
Task 3.1..............................................................................................................................9
Task 3.2............................................................................................................................10
Task 4 – Hypothesis Testing:...............................................................................................10
Task 4.1............................................................................................................................10
Task 4.2............................................................................................................................11
Task 5 – Correlation and regression:...................................................................................12
Task 5.1................................................................................................................................12
Task 5.2................................................................................................................................13
Task 5.3................................................................................................................................13
Task 5.4................................................................................................................................13
Conclusion:..............................................................................................................................14
References:...............................................................................................................................15
Appendices:..............................................................................................................................16
Task 3 – Confidence Interval:..............................................................................................16

2FINANCIAL STATISTICS
Task 4 – Hypothesis Testing:...............................................................................................16
Task 5 – Correlation and regression:...................................................................................17

3FINANCIAL STATISTICS
Tasks
Task 1:
The selected 60 random variables out of 2002 random variables are collected. The
option “Random Variable Generation” of “Data Analysis” toolpack is used for extracting
random variable.
Task 2:
Quantitative Variables:
Order Quantity
Mean 30.116667
Median 32
Mode 39
Standard Deviation 13.09171256
Variance 171.3929379
Minimum 2
Maximum 50
Range 48
Coefficient of Variation 43.46999%
1st quartile 19
3rd quartile 40.25
Inter quartile range 21.25
(Oja 1983)
The average value of the Order Quantity is 30.11667 with standard deviation 13.0917
and variance 171.3929. The maximum order quantity is 50 and minimum order quantity is 2
with the range 48. The calculated coefficient of variation is 43.4699%. The location
parameters show that 1st quartile, median (2nd quartile) and 3rd quartile values of order
quantity are 19, 30.11 and 40.25. The inter quartile range is found to be 21.25. The Order
Quantity of number 32 is maximum in frequency.
Sales
Mean $1,808.93

4FINANCIAL STATISTICS
Median $579.59
Mode #N/A
Standard Deviation $3,340.82
Variance $11,161,055.62
Minimum $30.10
Maximum $18,056.68
Range $18,026.58
Coefficient of Variation 184.68425%
1st quartile $185.93
3rd quartile $1,711.22
Inter quartile range $1,525.29
The average value of the Sales of Hardware and Gardens supplies is $1,808.93 with
standard deviation $3,340.82 and variance $11,161,055.62. The maximum order quantity is
$18,056.68 and minimum order quantity is $30.10 with the calculated range $18,026.58. The
calculated coefficient of variation is 184.68425%. The location parameters show that 1st
quartile, median (2nd quartile) and 3rd quartile values of order quantity are $185.93, $579.59
and $1,711.22. The inter quartile range is found to be $1,525.29. The mode is not found in
case of Sales data.
Shipping cost
Mean $13.69
Median $5.48
Mode $24.49
Standard Deviation $20.99
Variance $440.51
Minimum $0.49
Maximum $99.00
Range $98.51
Coefficient of Variation 153.27066%
1st quartile $1.99
3rd quartile $13.41
Inter quartile range $11.42
The average value of the Shipping cost of Hardware and Gardens supplies is $13.69
with standard deviation $20.99 and variance $440.51. The maximum order quantity is $99.00

5FINANCIAL STATISTICS
and minimum order quantity is $0.49 with the calculated range $98.51. The calculated
coefficient of variation is 153.27066%. The location parameters show that 1st quartile, median
(2nd quartile) and 3rd quartile values of order quantity are $1.99, $5.48 and $13.41. The inter
quartile range is found to be only $11.42. The Shipping cost of amount $24.49 has occurred
for maximum time than any other shipping costs.
Days to ship
Mean 2.283333
Median 2
Mode 2
Standard Deviation 2.067436525
Variance 4.274293785
Minimum 0
Maximum 9
Range 9
Coefficient of Variation 90.54467%
1st quartile 1
3rd quartile 2.25
Inter quartile range 1.25
The average value of the Days to ship of Hardware and Gardens supplies is 2.283
days with standard deviation 2.0674 and variance 4.27429. The maximum number of days to
ship is 9 days and minimum number of days to ship is 0 day with the calculated range of 9
days. The calculated coefficient of variation is 90.54467%. The location parameters show
that 1st quartile, median (2nd quartile) and 3rd quartile values of days to ship are 1 day, 2 days
and 2.25 days. The inter quartile range is 1.25 day. Most of the days to ship observed as 2
days.
Qualitative Variables:
Frequency Tables:
Order Priority Frequency Percentage
Not Specified 10 16.67%

6FINANCIAL STATISTICS
Low 18 30.00%
Medium 10 16.67%
High 9 15.00%
Critical 13 21.67%
Total 60 100.00%
The qualitative variable Order Priority refers maximum frequency (18, 30%) for
“Low” order priority followed by “Critical” Order Priority (13, 21.67%). The minimum
frequency has (9, 15%) for “High” order priority.
Ship Mode Frequency Percentage
Regular Air 49 81.6667%
Delivery Truck 7 11.6667%
Express Air 4 6.6667%
Total 60 100%
The qualitative variable “Ship Mode” indicates significantly maximum frequency (49,
81.667%) for “Regular Air” shipping mode. “Delivery Truck” (7, 11.667%) and “Express
Air” (4, 6.667%) have significantly lesser frequencies and percentages of frequencies than
“Regular Air”.
Region Frequency Percentage
Easter region 39 65.0000%
Western region 21 35.0000%
Total 60 100%
The qualitative variable “Region” shows that “Eastern region” has more occurrences
(39, 65%) than “Western region” (21, 35%).
Customer Segment Frequency Percentage
Consumer 11 18.3333%
Corporate 18 30.0000%
Small Business 17 28.3333%
Home Office 14 23.3333%

7FINANCIAL STATISTICS
Total 60 100.0000%
The “Customer Segment” refers that most of the customers are working in
“Corporate” with frequency 18 and percentage 30% followed by “Small Business” with
frequency 17 and percentage 28.33%. The minimum Customer Segment is observed in
“Corporate” (11, 18.33%).
Graphical Representation:
Not Specified Low Medium High Critical
0.00%
5.00%
10.00%
15.00%
20.00%
25.00%
30.00%
35.00%
16.67%
30.00%
16.67% 15.00%
21.67%
Line Diagram of percentages of Order Priority
Order Priority
Percentages
The Line Diagram shows the percentages of Order Priority

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Regular Air Delivery Truck Express Air
0.0000%
10.0000%
20.0000%
30.0000%
40.0000%
50.0000%
60.0000%
70.0000%
80.0000%
90.0000%
81.6667%
11.6667%
6.6667%
Histogram of percentages of Shipping Mode
The histogram of percentages of Shipping Mode
39; 65%
21; 35%
Pie cahrt of distribution of regions
Easter region
Western region
The Pie chart shows distribution of two different regions. The areas in the circle are
proportional to the two types of regions.

9FINANCIAL STATISTICS
Consumer Corporate Small Business Home Office
0.0000%
5.0000%
10.0000%
15.0000%
20.0000%
25.0000%
30.0000%
35.0000%
18.3333%
30.0000% 28.3333%
23.3333%
Bar plot of Customer Segment
Customer Segment
Percentages
The bar plot of Customer Segment dictates the percentages of four types of customer
segments. The heights of the bars are proportional to the percentages of types of customer
segments (Jelen 2010).
Task 3 – Confidence Interval:
The 95% Confidence limit with the help of Z-statistic is-
Z(0.05) * ( σ
√n )
The confidence intervals found with the help of one-sample Z-test is –
Xbar ±Z(0.05) * ( σ
√ n ) (Houghton Mifflin Harcourt, 2018)
Task 3.1
We are keen to find the average sales amount of orders for the “Home Office” only.
The average sale of 14 samples (Home Office) out of 60 samples (four types of customer
segments) is $677.95. The Standard error is $186.23. At the level of 5% significance, the

10FINANCIAL STATISTICS
confidence interval is $365.00. The calculated upper confidence limit and lower confidence
limits of “Sales” are $1042.95 and $312.94.
We are 95% confident that the average sales would lie in the interval ($312.94,
$1042.95) for home office customers.
Task 3.2
Next, we are interested to find the average shipping costs for all selected 60 sample-
orders. The average value of Shipping Cost is $13.69. The Standard error is $2.71. At 5%
level of significance, the confidence interval is $5.31. The calculated upper confidence limit
and lower confidence limits of “Shipping Cost” are $19 and $8.38.
We are 95% confident that the average shipping cost would lie in the interval ($8.38,
$19) for all sample orders.
Task 4 – Hypothesis Testing:
Task 4.1
It was realized that the Order Priority of “Critical” would have higher shipping costs than
an order of “Low” priority.
Hypotheses:
Null Hypothesis (H0): The shipping cost of “Critical” Order Priority is higher than or
equal to “Low” Order priority.
Alternative Hypothesis (HA): The shipping cost of “Critical” Order Priority is lesser
than “Low” Order priority.
Chosen Test:

11FINANCIAL STATISTICS
A Two-sample Z-test for equality of means is incorporated here for shipping costs of
two types of Order priority.
Level of Significance:
α=0.05
Inferential Statistic:
The Z-statistic is - z = ¿ ¿,
where,
x1bar and x2bar are two observed means.
μ1 and μ2 are two observed hypothetical averages.
n1 and n2 are numbers of two samples.
σ1 and σ2 are observed standard deviations of two samples.
The calculated Z-score for means of two samples is 0.53116.
p-Value:
The two-tail p-value for 95% confidence interval is 0.5953.
Conclusion:
Therefore, we accept the null hypothesis of greater or equality of shipping cost for
“Critical” Order Priority than “Low” Order Priority with 95% probability (Gardner and
Altman 1986).
Task 4.2
It is often felt that the mean values of order of sales in dollars, differs for Eastern states
(E) and Western states (W).

12FINANCIAL STATISTICS
Hypotheses:
Null Hypothesis (H0): The average sales of Eastern states and Western states are
equal.
Alternative Hypothesis (HA): The average sales of Eastern states and Western states
are unequal.
Chosen Test:
A Two-sample Z-test for equality of means is incorporated here for average sales of
two regions.
Level of Significance:
α=0.05
Inferential Statistic:
The Z-statistic is - z = ¿ ¿,
where,
x1bar and x2bar are two observed means.
μ1 and μ2 are two observed hypothetical averages.
n1 and n2 are numbers of two samples.
σ1 and σ2 are observed standard deviations of two samples.
The calculated Z-score for means of two samples is 1.7822.
p-Value:
The two-tail p-value for 95% confidence interval is 0.07472.

13FINANCIAL STATISTICS
Conclusion:
Therefore, we accept the null hypothesis of greater or equality of average sales for
both Eastern and Western regions with 95% probability.
Task 5 – Correlation and regression:
Task 5.1
0 10 20 30 40 50 60
$0.00
$2,000.00
$4,000.00
$6,000.00
$8,000.00
$10,000.00
$12,000.00
$14,000.00
$16,000.00
$18,000.00
$20,000.00
f(x) = 56.895782521414 x + 95.4229330634166
R² = 0.0497104621213912
Scatterplot of Sales vs. Order Quantity
Order Quantity
Sales
The scatter plot is constructed assuming Order quantity as independent and Sales as
dependent variable. The trend line of the scatter plot indicates that the data points are not
fitted well.
Task 5.2
The linear regression model is-
Y = α + β*X
Where, Y = dependent variable, X= independent variable, α = intercept, β = slope/
coefficient of independent variable

14FINANCIAL STATISTICS
According to the calculated linear regression model assuming “Sales” a dependent
and “Order Quantity” an independent variable, the linear regression model is –
Sales = 95.42293306 + 56.89578252 * Order Quantity
Task 5.3
The coefficient of correlation ( r ) is 0.222958431. It indicates a weak positive
correlation between Sales and Order Quantity (Samawi and Vogel 2014).
The coefficient of determination (R2) is 0.049710462. It shows that the linear
association is insignificant.
Task 5.4
The intercept (α) of the linear regression model is 95.42293306 and slope (β) of the
model is 56.89578252. For zero value of Order Quality, the Sales could be 95.42293306. For
per unit increment and decrement of Order Quantity, the Sales increases or decreased by
56.89578252 units. The positive value of the slope refers a positive relationship between
dependent and independent variable.
The p-value for F-statistic is 0.086836533. It is greater than 0.05. Therefore, Order
Quality has significant effect on Sales of Hardware or Garden samples.
The value of multiple R-square is 0.049710462 (4.9%). Therefore, only 4.9%
variability of Order Quality could be explained by Sales. The value of multiple R-square
refers that the fitting of the model is not good.
Conclusion:
The analysis helped to find descriptive statistics for quantitative variables. The graphs
and frequency tables are executed for qualitative variables. We tested 95% confidence

15FINANCIAL STATISTICS
intervals of two different quantitative variables (sales and shipping costs) both with and
without condition. We tested the hypotheses of equality and inequality of shipping costs for
two types of priorities. The higher value of shipping cost in case of Critical situation than
Low situation is found. The testing of equality of average sales for two types of regions is
also incorporated. The average sales or Eastern region and Western region are found equal.
Finally, the linear regression model is carried out assuming “Sales” a dependent and “Order
Quality” an independent variable. The linear association between two variables is found to be
insignificant.

16FINANCIAL STATISTICS
References:
Gardner, M.J. and Altman, D.G., 1986. Confidence intervals rather than P values: estimation
rather than hypothesis testing. Br Med J (Clin Res Ed), 292(6522), pp.746-750.
Houghton Mifflin Harcourt (2018). Two-Sample z-test for Comparing Two Means. [online]
Cliffsnotes.com. Available at: https://www.cliffsnotes.com/study-guides/statistics/univariate-
inferential-tests/two-sample-z-test-for-comparing-two-means [Accessed 6 Feb. 2018].
Jelen, B., 2010. Charts and Graphs: Microsoft Excel 2010. Que Publishing.
Oja, H., 1983. Descriptive statistics for multivariate distributions. Statistics & Probability
Letters, 1(6), pp.327-332.
Samawi, H.M. and Vogel, R., 2014. Notes on two sample tests for partially correlated
(paired) data. Journal of Applied Statistics, 41(1), pp.109-117.

17FINANCIAL STATISTICS
Appendices:
Task 3 – Confidence Interval:
Sales
mean $677.95
standard deviation $ 696.81
sample size 14
Standard error $ 186.23
Level of significance 0.05
Z-statistic 1.959964
Confidence interval (95%) $ 365.00
Upper confidence limit $1,042.95
Lower confidence limit $312.94
Shipping Cost
mean $13.69
standard deviation $20.99
sample size 60.00
Standard error $2.71
Level of significance 0.05
Z-statistic 1.959963985
Confidence interval (95%) $5.31
Upper confidence limit $19.00
Lower confidence limit $8.38
Task 4 – Hypothesis Testing:
Z-Test: Two Sample for Means
Critical Shipping
Cost Low Shipping Cost
Mean 16.86461538 12.10444444
Known Variance 872.8740603 237.0213791
Observations 13 18
Hypothesized Mean Difference 0
z 0.531168477
P(Z<=z) one-tail 0.297651018
z Critical one-tail 1.644853627
P(Z<=z) two-tail 0.595302035
z Critical two-tail 1.959963985

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Decision making Null hypothesis accepted
Z-Test: Two Sample for Means
Sales of Eastern
region Sales of Western region
Mean 2260.109436 971.0374762
Known Variance 15279794.97 2759388.95
Observations 39 21
Hypothesized Mean Difference 0
z 1.782164641
P(Z<=z) one-tail 0.037361194
z Critical one-tail 1.644853627
P(Z<=z) two-tail 0.074722387
z Critical two-tail 1.959963985
Decision making Null hypothesis accepted
Task 5 – Correlation and regression:
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.2229584
31
R Square
0.0497104
62
Adjusted R
Square
0.0333261
6
Standard Error
3284.6766
2
Observations 60
ANOVA
df SS MS F
Significanc
e F
Regression 1
32734452.7
3
327344
53
3.034029
83
0.08683653
3
Residual 58
625767828.
9
107891
00
Total 59 658502281.

19FINANCIAL STATISTICS
6
Coefficien
ts
Standard
Error t Stat P-value Lower 95%
Upper
95%
Intercept
95.422933
06
1071.23672
8
0.08907
7
0.929327
31
-
2048.89034
2239.736
2
Order Quantity
56.895782
52
32.6640590
4
1.74184
7
0.086836
53
-
8.48843503 122.28