Numeracy and Data Analysis: Calculation of Mean, Median, Mode, Range and Linear Regression Model for Temperature of London

This dissertation on Numeracy and Data Analysis provides insights on the calculation of Mean, Median, Mode, Range and Linear Regression Model for Temperature of London. It elaborates on statistical tools and steps of calculation for better understanding of the data. The subject is not mentioned.

Numeracy and Data
Analysis

Table of Contents
INTRODUCTION...........................................................................................................................1
MAIN BODY...................................................................................................................................1
Tabular data for temperature of London................................................................................1
Charts representing temperature.............................................................................................1
Compute the data with various statistical tools by elaborating its steps of calculation.........2
Compute the value of m and c using the linear forecasting model........................................5
CONCLUSION................................................................................................................................6
REFERENCES................................................................................................................................7

INTRODUCTION
In the following dissertation, the temperature of London is determined for the last 10 days
for assessing the descriptive statistics which are further divided as central tendency and measures
of variability. The data given below will initially be analysed and then all of the measures will be
calculated. In this manner, an individual can easily assess various set of data, no matter the size
for figuring out a specific value.
MAIN BODY
Tabular data for temperature of London.
Charts representing temperature.
1
Day Temperature
1 22
2 25
3 20
4 22
5 19
6 20
7 18
8 18
9 19
10 18
Total 201

Compute the data with various statistical tools by elaborating its steps of calculation.
a) Mean: In statistics, the arithmetic average or arithmetic mean is the total sum of a given
collection of data which is further divided by count of data collected. For instance, if an
individual wish to know the expectations related to average earnings of 20 financial
analysts covering for a particular stock group, then simply divide all proposed estimates
2
1 2 3 4 5 6 7 8 9 10
0
5
10
15
20
25
30 T em pera ture
1 2 3 4 5 6 7 8 9 10
0
5
10
15
20
25
Days
Tempera...

by 16, and that would be the arithmetic mean. (Takacs and Bourrat, 2022). Following is the
formula and procedure to calculate AM:
 Collect the data for relevant incident or event.
 Create a table for better understanding of the data.
 Number the data and calculate the sum of such data.
 Divide the above calculated sum by total no. of data collected.
From the above method and formula, the calculation for average temperature of London is made:
Mean = 201/10 = 20.1
Hence the average temperature of London for the above mentioned days, is 20.1 degrees.
b) Median: The probability theory, defines median as the value distinguishing the higher
half portion of sample data or population from the lower half of the same. For calculation
of median, it should be kept in mind that data is in ascending order (ELAIYARANI,
REVATHI, 2019). Following are the formula and steps for calculation:
 Arrangement of data in ascending order
 Determination of whether the data set is odd or even.
 The odd data set is handled by use of,
Median = N + ½
and for even data,
Median = N/2
Hence, data in ascending order would be,
18, 18, 18, 19, 19, 20, 20, 22, 22, 25
Median = (10+1)/2 = 5.5 or in middle of 5th and 6th position,
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hence, calculating mean for ascertaining the exact value of median class,
Mean = (19 + 20)/2 = 19.5
c) Mode: It is defined as one of the central tendency values, where the item which tends to
occur most in the data collected is characterised as mode. For example, if a college is
offering various courses for enrolled students then to find what course has the highest no.
of frequency in the given set of data is defined as mode (Johnston, and Faulkner, 2021).
Following are the formula and method:
 The arrangement of data should be made as per ascending or descending order.
 Determination of all the unique or distinct values in the given data set.
 After identifying the distinct data, whatever value has the highest amounts of repetitions
should be the mode.
Hence, the ascending data is,
18, 18, 18, 19, 19, 20, 20, 22, 22, 25
Mode = 18 which has the highest frequency.
d) Range: The calculation of range determines difference between the lowest and highest
value in a given data set which is usually used in statistics to spread the data from the
very lowest to the highest of values (Türkoğlu and Tuzcu, 2021). Following are the formula
and method for range calculation:
RANGE = HIGHEST VALUE – LOWEST VALUE
 Arrange the values in proper order or in ascending/descending manner.
 Find out the lowest and the highest value.
 Subtract the highest and lowest value determined before.
Hence, Range = Highest value – Lowest value
= 25 – 18 = 7
e) Standard Deviation: It is classified as a measure of variation amount or dispersion set of
values. It simply defines the average amount of variability in the collected dataset, or how
far the values lie from mean. A high standard deviation will indicate that the values lie far
from mean and vice versa for low standard deviation (Mikula, Petrusková and Albrecht,
2018). Following are the formula and method:
 Calculate the mean
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 Find deviation for each score from the mean
 Square each of the deviation from such mean
 Find the sum of the squares
 Find out the variance
 Lastly calculate the square root of above calculated variance.
Standard Deviation = √∑ (xi – μ) 2 / N = √136.9/10 = 13.69
= 3.7
Compute the value of m and c using the linear forecasting model.
The statistical method for prediction of future values from available past values is defined as
Linear Regression. The trends which are often involved in overvalued prices are determines
through this method (Sharan and Valiant, 2019). Following are the steps for the given theory:
 Reading and analysing the data.
 Visualizing the analysed data.
 Collecting necessary information.
 Application of calculated information for future prospects.
Here, the y = mx + c is defined for an equation of a line, which has a gradient or slope value
“m”, whereas “mx” being an independent factor, a y-intercept, where “y” is dependent factor and
“c” is a constant factor.
I. Calculation of “m”:
m = [10(1056) – (55*201)] / [10(385) – (55)^2]= - 805/3740 = - 0.215
II. Calculation of “c”:
= [201 - (-0.215(55))]/10
= 21.28
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III. Temperature on 11th day:
m= -0.215, c= 21.28, x=11
y = mx + c
y = -0.215(11) + 21.28 = 23.64
IV. Temperature on 14th day:
m = - 0.215, c = 21.28, x = 14
y = -0.215(14) + 21.28 = 18.27
CONCLUSION
As per the given information above, the temperature of a city is calculated as per the linear
regression model which provides forecasts related to the 11th and 14th day. Also the mean,
median and mode are calculated for performing the aforesaid analysis. The change in
temperature can easily be seen on 11th and 14th day, with 11th day being warmer as compared to
the 14th day. This being a perfect case to highlight importance of Linear Regression Forecasting
Method.
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REFERENCES
ELAIYARANI, M.K., REVATHI, M.M. and KEERTHANA, N., 2019. Performance analyzes of
RNS-FIR filter using prefix accumulation based DA arithmetic. Turkish Journal of
Computer and Mathematics Education (TURCOMAT), 10(3), pp.1064-1068.
Johnston, M.G. and Faulkner, C., 2021. A bootstrap approach is a superior statistical method for
the comparison of non-normal data with differing variances. New Phytol, 230(1), pp.23-
26.
Mikula, P., Petrusková, T. and Albrecht, T., 2018. Song complexity—no correlation between
standard deviation of frequency and traditionally used song complexity metrics in
passerines: A comment on Pearse et al.(2018). Evolution, 72(12), pp.2832-2835.
Sharan, V., Sidford, A. and Valiant, G., 2019, June. Memory-sample tradeoffs for linear
regression with small error. In Proceedings of the 51st Annual ACM SIGACT
Symposium on Theory of Computing (pp. 890-901).
Takacs, P. and Bourrat, P., 2022. The arithmetic mean of what? A Cautionary Tale about the Use
of the Geometric Mean as a Measure of Fitness. Biology & Philosophy, 37(2), pp.1-22.
Türkoğlu, S.P. and Tuzcu, S.E., 2021. Assessing country performances during the COVID-19
pandemic: A standard deviation based range of value method. Operational Research in
Engineering Sciences: Theory and Applications, 4(3), pp.59-81.
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