Numeracy and Data Analysis: Temperature Forecasting with Measures of Central Tendency and Linear Model

This report discusses the use of numerical methods to measure and analyze temperature in a country. It covers the concepts of mean, median, mode, range, and standard deviation to analyze the temperature data of the last 10 days. It also explains the use of a linear forecasting model to predict the temperature for upcoming days. The report concludes that the temperature will increase in the next two days.

Data Analysis and
Forecasting

Table of Contents
INTRODUCTION...........................................................................................................................2
MAIN BODY...................................................................................................................................2
CONCLUSION................................................................................................................................6
REFERENCES ...............................................................................................................................7
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INTRODUCTION
This file contain complete Data analysis forecasting on the Temperature of the country. All this
analysis is done by the helps of the methods and tools of Measures of central tendency such as
Mean, Mode, and Median and also use Linear forecasting Model to forecast the temperature of
upcoming days by the help of past values. A table showing below contains the temperature of
last 10 days in the country by the help of this data all the calculations has been done
easily(Madhavan and et.al., 2020).
MAIN BODY
1.
DAYS TEMPERATURE
1 12
2 10
3 13
4 14
5 14
6 15
7 15
8 13
9 13
10 13
TOTAL 132
3. Different Methods of Data Analysis are as follows :
a). Mean- It is the very first measures of central tendency, it is calculated by sum of given set of
data and divided by total number of given set of data(Sun and et.al., 2022). It is also known as
average of the given data. The formula for mean is-
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Mean= (Sum of all observation / total number of observation)
To find out the mean of the Temperature -
mean of Temperature= Sum of the given data / Total number of data
Mean= 132/10= 13.2
b) Median- It can be defined as the middle value of given set of data to find out the median the
data should be arrange in ascending and descending order(Tian and et.al., 2021). It is easy to find
if the number of given set of data are odd and if the number of given set of data are even then to
find the median middle two values must be divided by two.
The Formula to find out median if the given set of data is Odd-
Median= {(N+1)/2}th term
Formula to find out median when the Data is Even-
Median= (N/2)
where, N is Number of Observation.
To find out the Median some steps have to be followed-
rrange the data in ascending or descending order.
Days Temperature in degree
(Celsius)
1 12
2 10
3 13
4 14
5 14
6 15
7 15
8 13
9 13
10 13
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So, Median= 10+1 / 2
Median is= 5.5th position
Median=13+13
=26, 26/2 =13
so, Median=13.
c)Mode- The most repetitive value in the given set of data is known as mode(Yao and et.al.,
2020). It can be one, two or more than two. It is most easy measure of central tendency because
it can be find out by just observing the values.
Rearrange the data in Ascending and descending order. Then, just figure out the mode by
observing the most repetitive value in the given series.
Days Temperature Rearrange the data in
Ascending order
1 10 10
2 12 12
3 13 13
4 14 13
5 14 13
6 15 13
7 15 14
8 13 14
9 13 15
10 13 15
So most repetitive Number is 13
then 13 will be considered as Mode.
d)Range- The variation between the Highest and the lowest value of the given series called
Range.
Formula for Range= Largest value- Smallest value
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Range= 15-10
So, Range=5
e) Standard Deviation- It helps in measuring that how much data has been scattered in relation
with mean(Zhang and et.al., 2019). If the standard deviations is low it means the data is bunched
around the mean but if the standard deviation is high or the it means that the data is spread out
from the mean.
To calculate standard deviation the following steps are to be followed.
Days Temperature (X-X bar) (X-X)2
1 12 12-13.2 1.44
2 10 10-13.2 10.24
3 13 13-13.2 0.04
4 14 14-13.2 0.64
5 14 14-13.2 0.64
6 15 15-13.2 3.24
7 15 15-13.2 3.24
8 13 13-13.2 0.04
9 13 13-13.2 0.04
10 13 13-13.2 0.04
Total 132 19.6
Formula for Standard Deviation is-
Standard deviation= √∑ (xi – μ) 2 / N
=19.6/10
So, Standard deviation=1.96
Linear Forcing Model- This model helps the regulatory bodies to determine the upcoming
events by using the past values. It also helps in deciding the direction when costs are valuable.
Formula of Linear forcing model- (Y=mx+c)
where m is rate of change
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y is dependent factor.
mx is Independent factor.
and c is Constant factor.
Steps to calculate the linear Forcing Model-
Days Temperature xy x2
1 12 12 1
2 10 20 4
3 13 39 9
4 14 56 16
5 14 70 25
6 15 90 36
7 15 105 49
8 13 104 64
9 13 117 81
10 13 130 100
Total=55 132 743 385
m= (10*743)-(55*132) / (10*385-55*55)
m= (7430-7260) / (3850-3025)
m= 170/825
m= 0.20
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C= 132-0.20*55/10
=12.06
So the temperature on the 11th day will be:
m= 0.20, c=12.06, x=11
y=mx+c
y=0.20*11+12.06
so the temperature on Day 11 will be =14.26
Temperature on 12th day=
m=0.20, c=12.06, x=11
y=mx+c
y= 0.20*12+12.06
Temperature on 12th day= =14.46
CONCLUSION
From the above report it is concluded that the country use numerical methods to measure and
analyse the Temperature So according to mean the average temperature of the country is 13.2
and from mode it is understandable that temperature which is normally maintain from the last 10
days is 13 and from Range country observe that the temperature is increased by 5 degree Celsius
between 'day 2' to 'day 6' and by the help of linear casting model they can analyse the
temperature of upcoming days like what will be the temperature on day 11 and day12. So after
applying the linear forecasting country observe that the temperature will increase in next two
days.
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REFERENCES
Books and Journals
Madhavan and et.al., 2020. Short-term forecasting for airline industry: The case of Indian air
passenger and air cargo. Global Business Review. p.0972150920923316.
Sun and et.al., 2022. Improving Short-term Precipitation Forecasting with Radar Data
Assimilation and a Multiscale Hybrid Ensemble-Variational Strategy. Monthly Weather
Review.
Tian and et.al., 2021. Forecasting daily attraction demand using big data from search engines
and social media. International Journal of Contemporary Hospitality
Management. 33(6), pp.1950-1976.
Yao and et.al., 2020. Application of random forest algorithm in hail forecasting over Shandong
Peninsula. Atmospheric research. 244, p.105093.
Zhang and et.al., 2019. A novel hybrid model based on VMD-WT and PCA-BP-RBF neural
network for short-term wind speed forecasting. Energy Conversion and
Management. 195, pp.180-197.
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