Numeracy Report: Statistical Analysis of Manchester Wind Speed Data

This report provides a comprehensive analysis of Manchester's wind speed data from September 21st to 30th, 2019. The study begins by arranging the gathered dataset in a tabular format, followed by graphical representations using bar and line graphs. The report then delves into descriptive statistics, calculating the mean, median, mode, range, and standard deviation of the wind speeds. The steps for each calculation are clearly outlined. Furthermore, the report utilizes a linear forecasting model (y = mx + c) to predict wind speeds for day 14 and 21, including detailed steps for calculating the 'm' and 'c' values. The analysis concludes with a summary of findings and references to the sources used. This report effectively demonstrates the application of statistical tools in data analysis and forecasting.

Numeracy

TABLE OF CONTENTS
INTRODUCTION......................................................................................................................3
MAIN BODY.............................................................................................................................3
1. Arranging gathered dataset in a tabular format..................................................................3
2. Presenting dataset in a graphical format............................................................................3
3. Presenting steps of descriptive statistics along with the steps...........................................4
4. Calculating y = mx + c using linear forecasting model.....................................................8
CONCLUSION........................................................................................................................11
REFERENCES.........................................................................................................................13

INTRODUCTION
In the recent times, all the entities, whether related to business or not, lay high level of
emphasis on using statistical tools with the motive to derive suitable results. Moreover,
statistical tool clearly exhibits summary of large data set and thereby helps in making
effectual decisions. For this project report Manchester city of UK (West England) has been
selected. In this, report will provide deeper insight about the way in which mean, mode,
median etc pertaining to the wind speed of Manchester. Further, report will also provide
deeper insight about the wind speed of Manchester in relation to day 14 and 21.
MAIN BODY
1. Arranging gathered dataset in a tabular format
Data of Manchester’s wind speed km/hr from 21st to 30th September is as follows:
Date Wind speed km/hr
21st-Sep-2019 6
22nd-Sep-2019 6
23rd-Sep-2019 9
24th-Sep-2019 7
25th-Sep-2019 6
26th-Sep-2019 17
27th-Sep-2019 9
28th-Sep-2019 13
29th-Sep-2019 7
30th-Sep-2019 6
(Source: Past Weather in Manchester, England, United Kingdom — Yesterday and Last 2
Weeks, 2019)
2. Presenting dataset in a graphical format
Bar graph

21st-Sep-2019
22nd-Sep-2019
23rd-Sep-2019
24th-Sep-2019
25th-Sep-2019
26th-Sep-2019
27th-Sep-2019
28th-Sep-2019
29th-Sep-2019
30th-Sep-2019
0 2 4 6 8 10 12 14 16 18
Wind speed km/hr
Wind speed km/hr
Line graph
21st-Sep-2019
22nd-Sep-2019
23rd-Sep-2019
24th-Sep-2019
25th-Sep-2019
26th-Sep-2019
27th-Sep-2019
28th-Sep-2019
29th-Sep-2019
30th-Sep-2019
0
2
4
6
8
10
12
14
16
18
Wind speed km/hr
Wind speed km/hr
3. Presenting steps of descriptive statistics along with the steps
1. Computation of mean
Steps of mean assessment are enumerated below:
1. Computation of sum in relation to the wind speed of Manchester
2. Identifying the number of observation
3. Mean= sum of wind speed / number of days or observation

Date Wind speed km/hr
21st-Sep-2019 6
22nd-Sep-2019 6
23rd-Sep-2019 9
24th-Sep-2019 7
25th-Sep-2019 6
26th-Sep-2019 17
27th-Sep-2019 9
28th-Sep-2019 13
29th-Sep-2019 7
30th-Sep-2019 6
N = 10
Total (∑X) 86
Mean
∑X ÷ N
86 / 10
8.6
2. Median
Steps are as follows:
1. Firstly, setting all the data set in ascending manner
2. Applying the formula of (N + 1) / 2 (Amrhein, Trafimow and Greenland, 2019)
Here n implies for number of observation
3. As per the formula median value is derived by adding 5th and 6th value and then divide the
same from 2

Date Wind speed km/hr
21st-Sep-2019
6
22nd-Sep-2019
6
23rd-Sep-2019
6
24th-Sep-2019
6
25th-Sep-2019
7
26th-Sep-2019
7
27th-Sep-2019
9
28th-Sep-2019
9
29th-Sep-2019
13
30th-Sep-2019
17
Median 5.5
(N + 1) / 2 5.5
= 5.5 item
Median value
So, (Value of 5th item + value of 6th item) / 2
(7 + 7) / 2
7
3. Mode
In statistics, number which is repeated more frequently is considered as mode. Hence,
in the context of gathered data set regarding the wind speed of Manchester from 21st Sep to

30th mode value accounts for 6. Moreover, on the date of 21, 22, 25th and 30th Sep wind speed
km/hr was 6.
4. Range
Steps for assessing range
1. Determining highest value from data set
2. Assessing lowest value
3. Meanwhile, range can be determined by subtracting lowest value from the highest one
Particulars Figures
Maximum or highest wind speed level 17
Minimum or lowest wind speed level 6
Range
Maximum – Minimum value
17 – 6
= 11
5. Standard deviation
Steps of calculating SD is as follows:
1. Firstly, X^2 is calculated
2. Then, sum of the same need to assess
3. Sum of x^2 / number of observation
4. Thereafter, square of (∑x / n) is calculated (Amrhein, Trafimow and Greenland, 2018)
5. Outcome of step 3 – 4
6. SQRT of outcome derived in step 5
Date Wind speed km/hr X^2

21st-Sep-2019 6 36
22nd-Sep-2019 6 36
23rd-Sep-2019 9 81
24th-Sep-2019 7 49
25th-Sep-2019 6 36
26th-Sep-2019 17 289
27th-Sep-2019 9 81
28th-Sep-2019 13 169
29th-Sep-2019 7 49
30th-Sep-2019 6 36
Total 86 862
Standard deviation= SQRT of ∑x^2 / N – (∑x / n) ^ 2
= SQRT of (862 / 10) – (86 / 10) ^ 2
= SQRT of 86.2 – 73.96
= SQRT of 12.24
= 3.49
4. Calculating y = mx + c using linear forecasting model
1. Steps to calculate m value
Through following below mentioned steps value of m can be calculated
m = NΣxy – Σx Σy / NΣ x^2 – (Σx)^2
1. Summation of x*y is divided by number of observation
2. Thereafter Σx* Σy
3. Number of observation is multiplied by Σ x^2

4. Step 2 – step 1
5. Then, step 3 - (Σx)^2

6. Outcome derived in step 4 – step 5
2. Stages to compute c value
By undertaking following steps value of c can be determined:
1. In the first step, Σy is calculated
2. M is multiplied by Σx
3. Step 2 / number of observations
4. Σy – step 3
3. Assessing wind speed of Manchester in km/hr for day 14 and 21
Year
Number of year
(X)
Wind speed
km/hr (y) XY X^2
21st Sep 2019 1 6 6 1
22nd sep 2019 2 6 12 4
23rd Sep 2019 3 9 27 9
24th Sep 2019 4 7 28 16
25th Sep 2019 5 6 30 25
26th Sep 2019 6 17 102 36
27th Sep 2019 7 9 63 49
28th Sep 2019 8 13 104 64
29th Sep 2019 9 7 63 81
30th Sep 2019 10 6 60 100
Total 55 86 495 385

Particulars Formula Y = mX + c
M
m = NΣxy – Σx Σy / NΣ
x^2 – (Σx)^2
m = 10 (495) - (55 * 86) /
(10 * 385) – (55)^2
m = (4950 - 4730) / (3850 –
3025)
m = 220 / 825
m = 0.27
C c = Σy - mΣx / N
c = 86 – (.27 * 55) / 10
c = (86 – 14.85) / 10
c = 71.15 / 10
c = 7.11
Forecasting wind speed
km/hr for day 14
Y = mX + c Here x = day 14
Y = .27 (14) + (7.11)
Y = 3.78 + 7.11
Y = 10.89
Forecasting for day 21
Y = mX + c Here x = day 21
Y = .27 (21) + (7.11)
Y = 5.63 + 7.11
Y = 12.78
CONCLUSION
By summing up this report, it can be concluded that by taking into account the tool of
descriptive statistics weather department of Manchester can make effectual forecast about

future. In addition to this, using and summarize such data set high authority can develop
suitable plan about future.

REFERENCES
Books and Journals
Amrhein, V., Trafimow, D. and Greenland, S., 2018. Inferential statistics as descriptive
statistics: there is no replication crisis if we don't expect replication. PeerJ Preprints. 6.
p.e26857v4.
Amrhein, V., Trafimow, D. and Greenland, S., 2019. Inferential statistics as descriptive
statistics: There is no replication crisis if we don’t expect replication. The American
Statistician. 73(sup1), pp.262-270.
Online
Past Weather in Manchester, England, United Kingdom — Yesterday and Last 2 Weeks. 2019.
Online. Available through: <https://www.timeanddate.com/weather/uk/manchester/historic>