Statistical Analysis and Forecasting Report: Data Interpretation

This individual report presents a detailed analysis of a given dataset using various statistical techniques. The report begins with an introduction to data analysis, followed by a breakdown of the dataset presented in a tabular format. It then visualizes the data using column and line charts. The core of the report involves calculating and interpreting descriptive statistics, including mean, median, mode, range, and standard deviation. The report also applies a linear forecasting model to predict values for the 14th and 16th months. The conclusion summarizes the usefulness of statistical tools and techniques in extracting meaningful insights from raw data and making informed decisions, highlighting the importance of accurate application of these techniques. The report includes references to relevant books and journals.

Individual report

TABLE OF CONTENTS
INTRODUCTION......................................................................................................................3
MAIN BODY.............................................................................................................................3
1. Illustrating the data set in the form of table.......................................................................3
2. Plotting the data on graph..................................................................................................3
3. Presenting descriptive statistics table.................................................................................4
4. Predicting value for 14th and 16th month by making use of linear forecasting model.......7
CONCLUSION..........................................................................................................................9
REFERENCES.........................................................................................................................10

INTRODUCTION
Data analysis refers to the application of the analytical and logical reasoning to the
data available with the purpose of getting meaningful and relevant information about the data
set. This report highlights the application of the theoretical and practical application of eth
various methods and techniques in respect to the statistical analysis of the data. It will result
into building up the knowledge base which helps in effectively acquiring the crucial
information based upon which various decisions are taken. Along with that, it reflects upon
usefulness of various descriptive values derived.
MAIN BODY
1. Illustrating the data set in the form of table
Serial.
No. Date Amount of money spend on transport
(in pounds)
1 31-Mar-20 13
2 30-Apr-20 19
3 31-May-20 21
4 30-Jun-20 26
5 31-Jul-20 25
6 31-Aug-20 48
7 30-Sep-20 26
8 31-Oct-20 30
9 30-Nov-20 15
10 31-Dec-20 41
2. Plotting the data on graph
Column chart

1-Mar-20 1-Apr-20 1-May-20 1-Jun-20 1-Jul-20 1-Aug-20 1-Sep-20 1-Oct-20
0
5
10
15
20
25
30
35
40
45
50
13
19 21
26 25
48
26
30
Amount of money spend on transport (in pounds)
Line chart
1-Mar-20 1-Apr-20 1-May-20 1-Jun-20 1-Jul-20 1-Aug-20 1-Sep-20 1-Oct-20
0
10
20
30
40
50
60
13
19 21
26 25
48
26
30
Amount of money spend on transport (in
pounds)
3. Presenting descriptive statistics table
i. Mean value
Serial. No. Date Amount of money spend on transport
(in pounds)
1 31-Mar-20 13
2 30-Apr-20 19
3 31-May-20 21

4 30-Jun-20 26
5 31-Jul-20 25
6 31-Aug-20 48
7 30-Sep-20 26
8 31-Oct-20 30
9 30-Nov-20 15
10 31-Dec-20 41
Sum of the amount spend on
transport 264
Number of observations 10
Mean value 26.4
Interpretation
It can be stated that the mean value of the given data set is 26.4 which is being
determined through the way of taking the sum of eth amount spend and dividing it by the
number of observations (Dean and Illowsky, 2018).
ii. Median value
Step 1- Arranging the data in the ascending order
Serial.
No. Date Amount of money spend on transport
(in pounds)
1 31-Mar-20 13
2 30-Nov-20 15
3 30-Apr-20 19
4 31-May-20 21
5 31-Jul-20 25
6 30-Jun-20 26
7 30-Sep-20 26
8 31-Oct-20 30
9 31-Dec-20 41
10 31-Aug-20 48
Step 2- Determining value by applying the formula (n+1)/2
No. of
observation 10
M= (10+1) / 2 5.5
M= (25+26)/2 25.5
Interpretation:

The data has been arranged into ascending order which is important for deriving the
middle value called median and the value of median determined is 25.5 pounds (Zheng and
et.al., 2017).
iii. Mode value
Date Amount of money spend on transport
(in pounds)
31-Mar-20 13
30-Apr-20 19
31-May-20 21
30-Jun-20 26
31-Jul-20 25
31-Aug-20 48
30-Sep-20 26
31-Oct-20 30
30-Nov-20 15
31-Dec-20 41
Mode 26
Interpretation
Mode basically refers the most highly occurring number in the given data and in the
context to this data, the mode value is 26 as it occurred two times and the only number which
repeated.
iv. Range
Particulars Formula Amount
Maximum 48
Minimum 13
Range
Higher value - Smaller
value 35
Interpretation
Range simply accounts to the difference between the higher and the lower value of
the given data and is one of the measures of central tendency (Shi and et.al., 2020). In the
given data, the range of the data set is 35 pound and is also a good indicator of variability.
v. Standard deviation
Date Amount of money spend on transport
(in pounds) (X) X^2
31-Mar-20 13 195

30-Apr-20 19 625
31-May-20 21 441
30-Jun-20 26 676
31-Jul-20 25 625
31-Aug-20 48 2304
30-Sep-20 26 676
31-Oct-20 30 900
30-Nov-20 15 225
31-Dec-20 41 1681
Total 264 8348
Formula for determining standard deviation (SD) is stated below:
S.D = Square root of ∑x^2 / N – (∑x / n) ^ 2
= SQRT of (8348 / 10) – (264 / 10) ^ 2
= SQRT of 834.8 – 696.96
= SQRT of 137.84
= 11.74
Interpretation
SD measures the amount of spread of numbers from its mean values. Higher the
value, higher is eth level of risk and pertaining to this case, SD is 11.74 which is good as it is
not deviating much and prone to less risk.
4. Predicting value for 14th and 16th month by making use of linear forecasting model
Date X
Amount of
money spend
on transport
(in pounds)
(Y)
X*
Y X^2
31-Mar-20 1 13 13 1
30-Apr-20 2 19 38 4
31-May-20 3 21 63 9
30-Jun-20 4 26 104 16
31-Jul-20 5 25 125 25
31-Aug-20 6 48 288 36
30-Sep-20 7 26 182 49
31-Oct-20 8 30 240 64
30-Nov-20 9 15 135 81
31-Dec-20 10 41 410 100
Total 55 264
1,59
8 385

i. Determining the value of ‘m’
Formula to be used is:
m = NΣxy – Σx Σy / NΣ x^2 – (Σx)^2
Y = mX + c
m = 10(1598) - (55*264) / (10*385) – (55)^2
m = (15980 – 14520) / (3850-3025)
m = 1460/ 825 = 1.76
ii. Determining the value of ‘c’
c = Σy – m Σx / N
c = 264 – (1.76 * 55) / 10
c = (264 – 96.8) / 10
c = 167.2 / 10
c = 16.72
iii. Forecast for 14th and 16th month
Calculating the figure of Y by making use of m and c value
For 14th day-
Y = mX + c
= 1.76*14 + 16.72
= 24.64 + 16.72
= 41.36
For 16th day-
Y = mX + c
= 1.76*16 + 16.72
= 28.16 + 16.72
= 44.88
Interpretation
The linear forecasting model makes use of the equation y=mx + c for value of m and
C based upon which the amount is forecasted for the 14th and 16th month which appeared to
be 41.36 and 44.88 pounds respectively (Makridakis, Spiliotis and Assimakopoulos, 2018).

CONCLUSION
It can be inferred from the above that the statistical tools and techniques are useful in
deriving relevant information from the given data which one might not be able to get by
merely looking at the data. It has also resulted into making prediction about the future as
well. Data analysis is a very important technique which is being used by most of the
organization in order to derive useful information based upon which relevant business
decisions are take. It is crucial for the businesses to make sure that it has rightly applied the
techniques otherwise, it might result into getting wrong information.

REFERENCES
Books and Journals
Dean, S. and Illowsky, B., 2018. Descriptive statistics: skewness and the mean, median, and
mode. Connexions website.
Makridakis, S., Spiliotis, E. and Assimakopoulos, V., 2018. Statistical and Machine Learning
forecasting methods: Concerns and ways forward. PloS one. 13(3). p.e0194889.
Shi, J., and et.al., 2020. Optimally estimating the sample standard deviation from the five‐
number summary. Research Synthesis Methods. 11(5). pp.641-654.
Zheng, S., and et.al., 2017. The relationship between the mean, median, and mode with
grouped data. Communications in Statistics-Theory and Methods. 46(9). pp.4285-
4295.