Data Analysis Report: Statistical Analysis of Transportation Costs

This report presents a comprehensive data analysis of transportation expenditure over a ten-month period. It begins with organizing the data in a tabular format and then uses graphical representations to visualize the trends. The core of the report involves detailed calculations of key statistical measures, including the mean, median, mode, range, and standard deviation, providing interpretations of each value. Furthermore, the report constructs a forecasting model using a linear equation to predict transportation costs for future months, specifically the 14th and 16th months, demonstrating the application of statistical techniques in predicting future trends. The analysis includes the determination of 'm' and 'c' values within the linear equation and provides a concluding summary that emphasizes the importance of data analysis in decision-making processes.

NUMERACY AND DATA
ANALYSIS

Table of Contents
INTRODUCTION.......................................................................................................................................3
MAIN BODY..............................................................................................................................................3
1. Arranging data in tabular form:...........................................................................................................3
2. Graphical representation of data..........................................................................................................3
3. Representing the calculation................................................................................................................4
4. Preparing forecasting model for linear equation as follows:................................................................8
CONCLUSION.........................................................................................................................................10

INTRODUCTION
Data analysis refers to evaluating the available information in systematic manner for
interpreting the future course of action. In current scenario it is essential for business to have data
analytical skill for gaining competitive advantages. The current report will involve the systematic
presentation of data in tabular format along with graphical view of available information. Present
case study will show calculation of mean, mode, median, range and standard deviation. It will
discuss equation in understandable pattern.
MAIN BODY
1. Arranging data in tabular form:
S. No. Months Money incurred on
transportation expenditure (In
pounds)
1 Jan 10
2 Feb 15
3 Mar 5
4 April 45
5 May 51
6 June 42
7 July 34
8 Aug 24
9 Sept 24
10 Oct 25
2. Graphical representation of data

Jan Feb Mar April May June July Aug Sept Oct
0
10
20
30
40
50
60
Money incurred on transportation
expenditure
Jan Feb Mar April May June July Aug Sept Oct
0
10
20
30
40
50
60
Money incurred on transportation
expenditure
Money incurred on
transportation
expenditure
3. Representing the calculation
I. Computation of mean:
S. No. Months Money incurred on
transportation expenditure (In
pounds)
1 Jan 10
2 Feb 15

3 Mar 5
4 April 45
5 May 51
6 June 42
7 July 34
8 Aug 24
9 Sept 24
10 Oct 25
Total amount of money spent on transportation cost 275
Total number of months 10
Mean 27.5
Interpretation of mean value:
From the above formulated chart it can be interpreted that mean value of transportation expenses
is 27.5 pound. The formula applied for determining the mean is sum amount of money spend
divided by total of months which is 10.
II. Calculation of Median value
It can be determined by following two step method which is concerned with arranging
data in ascending order and then implementing formula:
Step 1: arrangement of available statistical information in ascending order
s. no Months Money incurred on
transportation expenditure (In
pounds)
1 Mar 5
2 Jan 10
3 Feb 15
4 Aug 24
5 Sept 24

6 Oct 25
7 July 34
8 June 42
9 April 45
10 May 51
Step 2: assessment of median value by implementing the formula (n+1)/2
Median (M) Number of observations 10
M (10+1)/2 5.5
(24+25)/2 24.5
Interpretation
From the above computed table it can be evaluated that median for the
transportation expenses is 24.5 pound. It is average of 5th and 6th month’s transportation
cost.
III. Determination of mode value
Months Money incurred on transportation expenditure
(In pounds)
Jan 10
Feb 15
Mar 5
April 45
May 51
June 42
July 34
Aug 24
Sept 24
Oct 25

On the basis of above table it can be analyzed that mode value is 24 as its frequency is
more than other observations (Fabián, 2021). The amount of transportation is repeating
twice so it is considered as mode in particular report.
IV. Computation of range value
Particulars Formula Amount
Maximum expense 51
Minimum expense 5
Higher expense- smaller
value
51-5= 46
Range is basically determined by deducting the smaller value from higher (Peleg, 2019).
From the above represented table it can be illustrated that maximum expense shown is 51
and lowest is 5. By analyzing the formula it is easily understood that it is difference
between the highest & lowest which has resulted into 46.
V. Standard Deviation (SD) calculation
Months Money incurred
(In pounds)
U (mean)
(27.5)
X-U (X-U)^2
Jan 10 27.5 -17.5 306.25
Feb 15 27.5 -12.5 156.25
Mar 5 27.5 -22.5 506.25
April 45 27.5 17.5 306.25
May 51 27.5 23.5 552.25
June 42 27.5 14.5 210.25
July 34 27.5 6.5 42.25
Aug 24 27.5 -3.5 12.25
Sept 24 27.5 -3.5 12.25
Oct 25 27.5 -2.5 6.25
Total 275 2110.5

SD= Square root of ∑(X-U)^2/N
= Square root of((2110.5)/10)
= SQRT OF 211.05
= £ 14.52
Interpretation:
Above calculation can be interpreted in following way. The derived value is £14.52
which is representing the moderate variation (Panigrahi and Behera, 2017). In addition to this,
this is an indication of moderate risk.
4. Preparing forecasting model for linear equation as follows:
Months X Y(Amount
spent on
transportation)
X*Y X^2
Jan 1 10 10 1
Feb 2 15 30 4
Mar 3 5 15 9
April 4 45 180 16
May 5 51 255 25
June 6 42 252 36
July 7 34 238 49
Aug 8 24 192 64
Sept 9 24 216 81
Oct 10 25 250 100
55 275 1638 385
i. Determination of m value:
m = NΣxy – Σx Σy / NΣ x^2 – (Σx)^2

=10(1638)- (55*275) /(10*385)- (55^2)
= 16380-15125/(3850)-3025
= 1255/825
m = 1.52
ii. Computation of value c is illustrated below
C = Σy – m Σx / N
275 – (1.52*55)/10
275-83.6/10
C= 19.14
iii. Showing computation of 14th and 16th month
Determination in case of 14th which is shown as below:
Y= mX +c
= 1.52(14)+19.14
=21.28+19.14
=£ 40.42
Computation in case of 16th day:
Y= mX +c
= 1.52(16)+19.14
= 24.32+19.14
= £ 43.46
Interpretation

From the above calculation it can be interpreted that m value is 1.52 and c has
19.14. These both are determined after substituting the value assessed from the
calculation into respective formulae (Liu and et.al., 2018.). By substituting the m and c’s
value into Y= mX +c transportation cost regarding 14 and 16 months has been
determined in respective form £40.42 & 43.46.
CONCLUSION
From the above report it can be concluded that how data analysis is crucial in making
decisions and coming to conclusion in easy manner. The present report has given
emphasis on various types of statistical calculation. Current case study has represented
the 10 months transportation cost in tabular form for making more reprehensive. In
addition to this, it has also involved the two types of graphical reflection of shown data in
column chart, etc. Computation of mean, mode, median , range , standard deviation has
been shown in report. Value derived are indicated in particular respective format. With
respect to this, the report has given focus on all required formulae for making calculation
more under stable. The current case study has comprised linear forecasting model. It has
involved the determination of m and c along with transportation cost for fourteen &
sixteen month.

REFERENCES
Books and Journals
Fabián, Z., 2021. Mean, mode or median? The score mean. Communications in Statistics-
Theory and Methods. 50(10). pp.2360-2370.
Liu, Y. and et.al., 2018. Artificial combined model based on hybrid nonlinear neural network
models and statistics linear models—research and application for wind
speed forecasting. Sustainability. 10(12). p.4601.
Panigrahi, S. and Behera, H. S., 2017. A hybrid ETS–ANN model for time series
forecasting. Engineering Applications of Artificial Intelligence. 66. pp.49-
59.
Peleg, M., 2019. Beta distributions for particle size having a finite range and predetermined
mode, mean or median. Powder Technology. 356. pp.790-794.