Numeracy and Data Analysis: Temperature Data Set Analysis

This report analyses the temperature data set of Liverpool, UK for 10 successive days using statistical tools such as mean, median, mode, range and standard deviation. Linear Forecasting Model has been used to predict the future temperatures of day 11 and 14.

Data Analysis

Table of Contents
Table of Contents.............................................................................................................................2
INTRODUCTION...........................................................................................................................3
MAIN BODY...................................................................................................................................3
1. Position the temperature data set in a table format..................................................................3
2. Present the temperature data set with the help of any two different kinds of graphs
accordingly...................................................................................................................................3
3. Compute the mean, median, mode, range and standard deviation of the temperature data set
with the description of steps required for calculation..................................................................5
4. For the data set, compute values of 'm' and 'c' and display the use of the required steps. With
the help of values of 'm' and 'c', predict the temperature for day 11 and 14................................7
CONCLUSION................................................................................................................................8
REFERENCES................................................................................................................................9

INTRODUCTION
Numeracy is defined as the subject matter that helps students to apply mathematics in wide range
of situations with the help of certain tools, methods, knowledge, skills and behaviours (Belotto,
2018). The temperature of Liverpool, UK for 10 successive days is mentioned. It has helped to
calculate the statistical tools such as mean, mode and median also the range and standard
deviation of the data set. Also the Linear Forecasting Model has been used and applied to
calculate and predict the future temperatures of day 11 and 14 with the assistance of the data set
already present.
MAIN BODY
1. Position the temperature data set in a table format.
Dates Temperature
1 20
2 20
3 22
4 18
5 18
6 15
7 16
8 17
9 18
10 17
TOTAL 181
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2. Present the temperature data set with the help of any two different kinds of graphs
accordingly.
5
31/12/1899
01/01/1900
02/01/1900
03/01/1900
04/01/1900
05/01/1900
06/01/1900
07/01/1900
08/01/1900
09/01/1900
0
5
10
15
20
25
Temperature (y)
0
5
10
15
20
25
Temperature (y)

3. Compute the mean, median, mode, range and standard deviation of the temperature data set
with the description of steps required for calculation.
Mean: The mean of a data set is calculated with the help of adding all the values and
dividing it by the total number of values that are there in the data set (Bergin, 2018).
Steps for calculating Mean of data set:
Step1: Collect the entire data set.
Step2: Find the sum of the all numbers by adding all the values.
Step3: Find the number of values in the set.
Step4: Divide the sum with number of values in set.
Mean of the Temperature = Sum of all given temperature data sets / Total values in the
given data set
=> 181 / 10
Mean of the Temperature => 18.1
Median: It is the middle most, centre position value of the entire data set when arranged
in an ascending order (Mihas, 2019).
Steps for calculating Median of data set:
Step1: Sort the data set in ascending order.
Step2: Find the data set is even or odd in terms of total number of values in the data set.
Step3: Apply the formula respectively:
n = odd : (n+1)th / 2
n = even : [(n/2)th term + ((n/2)+1)th term] / 2
In this case,
Data set :- 15 16 17 17 18 18 18 20 20 22
Median Value of the temperature (even) = [(n/2) term + ((n/2) + 1) term] / 2
= 10 / 2 term + (10/2+ 1) term / 2
= 5th value + 6th value / 2
= (18 + 18) / 2
Median of the Temperature => 18
Mode: It is the value that occurs the most number of times in the data set.
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Steps for calculating Mode of data set:
1: Sort the given data set in ascending order.
2: Count the number that occurs the most in the set.
3: The number that occurs the most is the mode of the set.
Data set :- 15 16 17 17 18 18 18 20 20 22
Mode of the Temperature=> 18
Range: It is the deviation between the highest and lowest value of the data set (Miles,
Huberman and Saldaña, 2018).
Steps for calculating Range of data set:
1: Observe the data set.
2: Take the highest and the lowest value.
3: Find difference between the two values.
Computation of Temperature Range
Range of data set = Highest value – Lowest Value
= 22 - 15
Range of the Temperature => 7
Standard Deviation: It is a measure to calculate and analyse how disperse each value is
of the data set from the mean value of the data set.
Steps for calculating Standard deviation of data set:
1: Look for the mean value.
2: Find dispersion of each value from the mean.
3: Square each and every deviation value and find its sum.
4: Divide the square from total number of values in the data set.
5: Take square root of the resulting numbers.
Calculation of standard deviation of Temperature:
Standard Deviation = √∑ (xi – μ) ^ 2 / N
=√ (181 – 18.1) ^ 2 / 10
Standard Deviation of the Temperature = 51.513
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4. For the data set, compute values of 'm' and 'c' and display the use of the required steps. With
the help of values of 'm' and 'c', predict the temperature for day 11 and 14.
Linear Forecasting Model: This model helps to predict the future values of the data set
with the assistance of the past values of data set that already occur (Tiwary and et.al., 2019).
Linear Forecasting theory steps are as follows:
Step1: Observe what is the problem.
Step2: Collect data through survey.
Step4: Choose the model that is suitable for the need.
Step5: Analyse the problem carefully.
y = mx + C
where, 'y' =Dependent Factor,
'mx' =Independent factor and
'c' =constant factor
Steps to calculate 'm':
Step1: Multiply, total number of data set with 'x' and 'y' variables.
Step2: Compute the sum of 'x' and 'y' separately and multiply them.
Step3: Multiply square value of x with total number of data.
Step4: Then calculate sum of 'x' and square that value.
Step5: Afterwards, subtract step2 from step1 and step4 from step3.
Step6: Finally, Divide the value of Step5 with Step6.
= 10 * 958 – (55 * 181) / 10 * 385 – 3025
= 9580 – 9955 / 825
m = 0.4545
Steps to calculate 'c’:
Step1: Add values of 'y' variable
Step2: Multiply the 'm' value with the sum of the values of 'x' variable.
Step4: Find the variation between Step2 and Step1.
Step5: Find the number of values
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Step6: Afterwards, divide the result of step3 by step5.
= 181 – 0.45 * 55 / 10
C = 15.625
Temperature Day 11:
m = 0.45, x = 11, C = 15.625
y = mx + C
= 0.45 * 11 + 15.625
y = 20.575
Temperature Day 14:
m = 0.45, x = 14, C= 15.625
y = mx + C
= 0.45 * 14 + 15.625
y = 21.925
CONCLUSION
The report above has calculations of mean, median and mode for the 10 consecutive days’
temperature data set. Calculations for range and standard deviation for the data set are also
completed. Graphs have been used to depict the temperature for 10 consecutive days. The report
contains the understanding of linear forecasting model and calculation of variables and
temperatures of day 11 and day 14 with the help of the data set already present is also done. All
of the above prospects have been explained thoroughly with the help of steps needed to calculate
the required variables.
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REFERENCES
Books and Journals
Belotto, M.J., 2018. Data analysis methods for qualitative research: Managing the challenges of
coding, interrater reliability, and thematic analysis. The Qualitative Report, 23(11),
pp.2622-2633.
Bergin, T., 2018. An introduction to data analysis: Quantitative, qualitative and mixed methods.
Sage.
Mihas, P., 2019. Qualitative data analysis. In Oxford research encyclopedia of education.
Miles, M.B., Huberman, A.M. and Saldaña, J., 2018. Qualitative data analysis: A methods
sourcebook. Sage publications.
Tiwary, S and et.al., 2019. High-quality MS/MS spectrum prediction for data-dependent and
data-independent acquisition data analysis. Nature methods, 16(6), pp.519-525.
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