Data and Numerical Analysis

This assignment explores data and numerical analysis in the context of forecasting weather. It covers topics such as calculating mean, median, mode, range, and standard deviation, as well as using a linear forecasting model. The data used is related to wind speed in London.

Data and Numerical
Analysis

Table of Contents
INTRODUCTION...........................................................................................................................1
Main Body.......................................................................................................................................1
1. Table Format......................................................................................................................1
2. Graphical representation of weather report........................................................................2
3. Calculation..........................................................................................................................3
4. Liner-forecasting model.....................................................................................................5
CONCLUSION................................................................................................................................6
REFERENCES................................................................................................................................8

INTRODUCTION
Data and numerical analysis can be defined as a way of organising and analysing a
statistical information to conclude the appropriate result (Ashby, 2019). The aim behind
interpreting a data is to forecast the information for upcoming period. For this purpose, a number
of statistical methods can be used for measuring the central tendencies i.e. organising the entire
data into single form so that future result can be estimated. Under this assignment, data which is
related to wind speed of some consecutive days of London is taken, for forecasting the report of
upcoming days. In this regard, some statistical methods are used to find mean, median, mode,
standard deviations and range, by representing the information into tabular and different
graphical form.
Main Body
To forecast the wind speed of upcoming days within era of London, data of last ten days
i.e. from 6th to 15th Dec. 2019 is taken. After then information is presented in tabular form with
some graphical representation as shown below -
1. Table Format
Wind speed Report from consecutive days of London area:
Days
Wind
At 12 PM
06/12/19 29 km/hr
07/12/19 18 km/hr
08/12/19 31 km/hr
09/12/19 25 km/hr
10/12/19 30 km/hr
11/12/19 15 km/hr
12/12/19 20 km/hr
13/12/19 29 km/hr
14/12/19 29 km/hr
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15/12/19 22 km/hr
2. Graphical representation of weather report
Wind speed
Days
Wind
At 12 PM
06/12/19 29 km/hr
07/12/19 18 km/hr
08/12/19 31 km/hr
09/12/19 25 km/hr
10/12/19 30 km/hr
11/12/19 15 km/hr
12/12/19 20 km/hr
13/12/19 29 km/hr
14/12/19 29 km/hr
15/12/19 22 km/hr
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3. Calculation
To calculate the weather data of London, the entire information is firstly converted into
form of central tendencies i.e. mean, median, mode, range and standard deviation by using
following formulae -
Mean: The statistical mean can be defined as an average of a data which is mainly used for
deriving central tendency into single form. This would can be calculating by adding all the
observation and then dividing the result from number of observations in following manner -
[ Mean/ Average = ∑x / N ] where, ∑x refers to the sum of total data points or observations
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While, N shows the total number of data points or observation
Median: The term median refers to a simple central tendency which divides the entire
population into two equal parts equally. For this purpose, data firstly rearranged from smallest to
largest to calculate middle data as described below –
if number of observation is odd then,
[ Median = (Number of days + 1) / 2 ]
Or, if number of observation is even then
[ Median = No. of days / 2 ]
Mode: The mode of a set of observation provides the value which is appeared often most. In
other words, observation which has highest frequency or is more likely to be sampled is known
as mode.
Range: This statistical method indicates the difference among observations by subtracting the
maximum data value to minimum as -
Range = Maximum data value – Minimum data value
Standard Deviations: It can be defined as the measure of amount of dispersion or variation
among set of data values. It can calculated by using following formula -
Standard Deviation =√ (variance)
Variance2 = {∑(x – mean) / N} 2
Calculation for Wind speed in km/hr
Days
Wind km/h in
London
06/12/19 29
07/12/19 18
08/12/19 31
09/12/19 25
10/12/19 30
11/12/19 15
12/12/19 20
13/12/19 29
14/12/19 29
15/12/19 22
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Mean 24.8
Median 27
Mode 29
Standard
deviation 5.6921
Calculation -
Mean = (Total Sum of Observation) / Number of observation
= 248 / 10
= 24.80 km/hr
Median = 10 / 2
= 5th Observation
= 27 km/hr
Mode = 29 km/hr (as it is repeated three times)
Range = Max – Min
= 29 – 15
= 14 km/hr
Standard Deviations = square root of variance
Where, Variance 2 = [ ∑(x – mean) / N ]2
= [ ∑( x2 / N – (mean)2 ]
= (6442 / 10 – (24.80) 2 )
= 644.2 – 615.04
= 29.16
Std Dev. = √29.16
= 5.4 km/hr approx..
4. Liner-forecasting model
This model is mainly used for predicting the future data value of a defined set of
observations, by using the below linear equation-
y = mx + c
here, m represents the slope of a line to describe the relationship between variables in following
way -
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m = Change in Y / Change in X
using the given wind speed table –
Days
Wind km/h in
London
06/12/19 29
07/12/19 18
08/12/19 31
09/12/19 25
10/12/19 30
11/12/19 15
12/12/19 20
13/12/19 29
14/12/19 29
15/12/19 22
Let y1 = 29 km/hr and, y0 = 18 km/hr
Then, value of x = 1 day
so, m = 29 – 18 / 1
= 11
Since, c in the given linear model always taken as constant therefore, any changes in variables do
not affect it. So, c can be calculated in following manner -
c = y – mx
= 11 – 11 / 1 = 0
Thus, by calculating the value of 'm' and 'c' in above linear equation, the value of wind can be
forecasted for upcoming days by using FORECAST.LINEAR tool (x,y
knownvalues,xknownvalues) as:-
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CONCLUSION
From this entire statistical report, it has been summarised that for analysing and
predicting the particular information, a number of statistical methods can be utilised. This would
help in forecasting the weather of upcoming days through which information to airlines and other
industry whose operations are mostly affected by weather condition can be provided.
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REFERENCES
Books and Journals
Ashby, F. G., 2019. Statistical analysis of fMRI data. MIT press.
Linz, P., 2019. Theoretical numerical analysis. Courier Dover Publications.
Mirzapour, F. and et. al., 2019. A new prediction model of battery and wind-solar output in
hybrid power system. Journal of Ambient Intelligence and Humanized
Computing. 10(1). pp.77-87.
Mori, R., 2019. Analysis of Speed Prediction Error on Oceanic Flights. The Journal of
Navigation. 72(6). pp.1469-1480.
Guo, Y. and van de Lindt, J., 2019. Simulation of hurricane wind fields for community resilience
applications: A data-driven approach using integrated asymmetric Holland models for
inner and outer core regions. Journal of Structural Engineering. 145(9). p.04019089.
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