Numeracy and Data Analysis: Forecasting Temperature in London

This report presents a comprehensive analysis of temperature data collected for the city of London, UK. It includes descriptive statistics such as mean, median, mode, range, and standard deviation to understand the central tendency and variability of the data. Furthermore, it applies a linear forecasting model to develop a regression equation and predict future temperatures for day 11 and day 14. The report details the steps involved in computing key parameters for the forecasting model, including the calculation of 'm' (slope) and 'c' (constant). The findings offer insights into temperature trends and demonstrate the application of statistical methods for forecasting purposes. Desklib provides a platform to access similar solved assignments and study tools for students.

NUMERACY AND
DATA ANALYSIS

Table of Contents
INTRODUCTION.......................................................................................................................3
TASK........................................................................................................................................3
Organise the data in a format of table...............................................................................................3
Represent the data with the help of any two sort of charts...............................................................3
Compute and explain the terms stated as under. Also provide steps for the computation and
highlight the final recorded value......................................................................................................5
With the assistance of linear forecasting model compute and describe the following:......................7
Explain the steps to compute value of m...........................................................................................7
Describe the steps involved during the computation of c value.........................................................8
With the help of computed values of ‘m’ and ‘c’ values, carry out the forecasting related to
temperature for day 11 and day 14....................................................................................................8
CONCLUSION...........................................................................................................................9
REFERENCES...................................................................................................................................10

INTRODUCTION
The report prepared as under is useful to collected informative data that would prove to be a
useful tool for acquiring the idea about what is being done. The information in a report is
collected for city of London that is situated in UK (Beller and Wagner, 2020). It has also
considered carrying out descriptive statistics which is being performed on data gathered. Further
it has also provided assistance in computing regression equation that would be formed and
forecasting of 2 days can be carried out with the help of equation.
TASK
Organise the data in a format of table.
Represent the data with the help of any two sort of charts.

The above developed chart is a column chart which would be representing the level of
temperature for 10 consecutive days.
ˇ
The above prepared chart is observed to be in the form of line chart which represents the
temperature on regular basis which is helpful in plotting the level of temperature on a regular
basis with the help of trend line.

Compute and explain the terms stated as under. Also provide steps for the computation and
highlight the final recorded value.
 Mean: It can be defined as average number which is related to value for which data is
being gathered at one place (Fernandez and Liu, 2019). In above collected data the
average outcome of temperature is calculated for 10 consecutive days.
Steps which are considered for calculation of mean:
Step 1: Find all the factors which are given.
Step 2: Summation of all values must be done.
Step 3: Tally the summation of observation against total number of explanations.
Mean = Summing of observations/Total number of observations
Mean = 176/10 = 17.6
 Median: It can be defined as all type of collected information and data in ascending order.
It can be explained as a middle factor in the series being developed and is also denoted as
median.
Steps for calculating Median:
Step 1: Firstly, arrange all the gathered information and data in ascending order.
Step 2: Afterwards calculate the number of observations for understanding whether it is odd
or even.
Step 3: If the series has found to be even then implement formula (n/2).
Step 4: If it proves to be odd then the formula which must be used is (n+1/2).
Step 5: The outcome which is being recorded is denoted as median.
Median = (n+1)/2
= (10+1)/2
= 11/2 = 5.5
10, 7, 11, 15, 24, 16, 25, 30, 27, 11
7, 10, 11, 11, 15, 16, 24, 25, 27, 30
So, the median after computation is found (15+16)/2 = 15.5
 Mode: It can be explained as a factor, element or value which is observed to take place
frequently in a dataset.
Steps involved in computation of mode:

Step 1: Gather and sort the data which is collected as under.
Step 2: Search which is a different value.
Step 3: Tally the frequency for the value which is observed to occurr at a higher range from
the data series.
Step 4: Highest frequency observed is considered as Mode.
7, 10, 11, 11, 15, 16, 24, 25, 27, 30
It is hence observed from the above data series that the figure which seems to be occurring
most of the time is 11. It has appeared twice.
 Range: It explains the difference between largest number and smallest number to
understand the variation.
Steps for calculation of range:
Step 1: Sort all the information which is available.
Step 2: Find out which one in the series prepared is high and low in terms of value.
Step 3: Subtract the least digit from the highest figure.
Step 4: The figure which is being recorded after the step 3 is denoted as range.
Range = Maximum value – Minimum value
Range = 30 – 7 = 23.
 Standard deviation:
Steps involved in calculation of Standard deviation
Step 1: At first place find the mean of stated data series.
Step 2: For every observation find the deviation present among the value and the mode of the
value.
Step 3: Sum all values from Step 2.
Step 4: Carry out division by number of terms (n).
Step 5: Finally, square root the outcome which is being observed in Step 4.
Standard deviation
Day Temperature xi - μ (xi - μ)2
1 10 -7.6 57.76
2 7 -10.6 112.36
3 11 -6.6 43.56
4 15 -2.6 6.76
5 24 6.4 40.96
6 16 -1.6 2.56

7 25 7.4 54.76
8 30 12.4 153.76
9 27 9.4 88.36
10 11 -6.6 43.56
176 2.84 604.4
Standard Deviation= √ (xi – μ)2 / N
= √ (604.4) / 10
= √ 60.44
= 7.77
With the assistance of linear forecasting model compute and describe the following:
Linear forecasting model: It is useful in predicting ‘futuristic results’ which are based on ‘past
values’ in a linear equation formed so far.
y = mx + c
Here, ‘y’ is denoted as dependent variable
‘mx’ is the independent variable
‘c’ is depicted as constant.
Explain the steps to compute value of m.
Steps involved in calculation of m is:
1. Multiplication of both the factors X and Y which are denoted as temperature and days.
2. Figure out the summation for above calculation.
3. Add x factor and y factor on a individual basis.
4. Then, multiplication of both the counted elements must be done.
5. Compute (x)2 and in the end, place put all the values in formula used.
6. The outcome observed will be the value of ‘m’.
M =
Linear forecasting model
Day Temperature xy x^2
1 10 10 1
2 7 14 4

3 11 33 9
4 15 60 16
5 24 120 25
6 16 96 36
7 25 175 49
8 30 240 64
9 27 243 81
10 11 110 100
55 176 1101 385
m = √ (10 * 1101) – 1101 / [10* 385 – (385)]
= (11010 - 1101) / 3850 – 385
= 9909 / 3465
= 2.86
The above value of m denotes the slope of the line which is 2.86.
Describe the steps involved during the computation of c value.
Steps for calculation of c:
1. Firstly, calculate the sum of ‘y’ variable.
2. Afterwards, compute the summation of ‘x’ element.
3. Divide it by the summation of ‘N’.
4. The value which would be recorded from step 3 would be the value of ‘c’.
C =
c = 176 – (2.86 * 55) / 10
= (176 – 157.3) /10
= 18.7 / 10 = 1.87
With the help of computed values of ‘m’ and ‘c’ values, carry out the forecasting related to
temperature for day 11 and day 14.
Temperature on day 11:
m = 2.86, c = 1.87, x = 11,
y = mx + c

y = (2.86 * 11) + 1.87
y = 31.46 + 1.87
y = 33.33
Temperature on Day 14:
m = 2.86, c = 1.87, x = 14,
y = mx + c
y = (2.86 * 14) + 1.87
y = 40.04 + 1.87
y = 41.91
CONCLUSION
From the above computed information, it can be concluded that the data of temperature is
examine with the assistance of mean, mode, median, range and standard deviation. It also helped
to forecast the future temperatures with the help of regression equation which has been
developed with the help of linear forecasting model.

REFERENCES
Books and Journals
Beller, J. and Wagner, A., 2020. Loneliness and health: the moderating effect of cross-cultural
individualism/collectivism. Journal of Aging and Health, 32(10), pp.1516-1527.
Fernandez, F. and Liu, H., 2019. Examining relationships between soft skills and occupational
outcomes among US adults with—and without—university degrees. Journal of
Education and Work, 32(8), pp.650-664.
Joseph, P. and Fleary, S.A., 2021. “The way you interpret health”: Adolescent definitions and
perceptions of health literacy. Journal of School Health, 91(8), pp.599-607.
Marks, G.N., 2020. Is the relationship between socioeconomic status (SES) and student
achievement causal? Considering student and parent abilities. Educational Research and
Evaluation, 26(7-8), pp.344-367.
Ndijuye, L.G. and Rao, N., 2019. Early reading and mathematics attainments of children of self-
settled recently naturalized refugees in Tanzania. International Journal of Educational
Development, 65, pp.183-193.