Statistical Analysis and Forecasting of Lewisham Wind Speed Data

This assignment provides a comprehensive analysis of Lewisham wind speed data collected over a ten-day period. The student begins by organizing the data in a structured format and presenting it graphically using line and column charts. The core of the analysis involves calculating descriptive st...Read More

Numeracy and Data

TABLE OF CONTENTS
INTRODUCTION......................................................................................................................3
1. Arranging data in a structured format................................................................................3
2. Graphical presentation of data set......................................................................................3
3. Calculating descriptive statistics of Lewisham wind speed data and showing steps of
calculation..............................................................................................................................4
4. Doing forecast by using linear method of statistics...........................................................7
CONCLUSION..........................................................................................................................9
REFERENCES.........................................................................................................................10

INTRODUCTION
Data analysis includes statistical tools and techniques which in turn help in analyzing
numeric facts & figures effectually. Statistical tools are highly significant as it helps in
evaluating present and making forecast about future. For this project report Lewisham of
London has been selected. This study will provide insight about weather condition in terms
of wind speed pertaining to Lewisham.
1. Arranging data in a structured format
Data of Lewisham wind speed (10 consecutive days) from 30th September to 9th October is
presented below:
Date Km/h
30-Sep 20
01-Oct 27
02-Oct 5
03-Oct 22
04-Oct 5
05-Oct 12
06-Oct 16
07-Oct 15
08-Oct 22
09-Oct 21
(Source: Lewisham weather data. 2019)
2. Graphical presentation of data set
Line graph

30-Sep
01-Oct
02-Oct
03-Oct
04-Oct
05-Oct
06-Oct
07-Oct
08-Oct
09-Oct
0
5
10
15
20
25
30
Km/h
Km/h
Column graph
30-Sep 01-Oct 02-Oct 03-Oct 04-Oct 05-Oct 06-Oct 07-Oct 08-Oct 09-Oct
0
5
10
15
20
25
30
Km/h
Km/h
3. Calculating descriptive statistics of Lewisham wind speed data and showing steps of
calculation
i. Mean
Step 1: Firstly, need to determine the number of observation
Step 2: Total of wind speed (km/hr) pertaining to 10 days are calculated
Step 3: At this stage, mean value can be determined by dividing ∑X from n (Sclove, 2018)
Date Km/h
30-Sep 20

01-Oct 27
02-Oct 5
03-Oct 22
04-Oct 5
05-Oct 12
06-Oct 16
07-Oct 15
08-Oct 22
09-Oct 21
(∑X) 165
Number of
observations 10
Mean
165 /
10 =
16.5
Referring evaluation, it can be presented that during the period of past days from 30th
September to 9th October average speed of wind was 16.5km/hr.
ii. Median
Step 1: Arranging data set in an ascending manner:
Date Km/h
30-Sep 5
01-Oct 5
02-Oct 12
03-Oct 15
04-Oct 16
05-Oct 20
06-Oct 21
07-Oct 22
08-Oct 22
09-Oct 27
Step 2: M = (number of observation + 1) / 2
Accordingly:
Number of observation = 10
M = (10 + 1) / 2
= 5.5

Step 3: Thus, m = (value of 5th + 6th item) / 2
M = (16 + 20) / 2
= 36 / 2
= 18 km / hr
From assessment, it has found that 50% value from gathered data set is related to the
figure of 18 km/hr.
iii. Mode
The above mentioned data set clearly exhibits that mode value implies for 5and 22
km/hr. Moreover, among 10 observations these values occurred twice so it considered as
mode. As, on 30th September and 1st October speed of wind in Lewisham was 5 km/hr.
Besides this, on 7th and 8th October wind speed implies for 22 km/hr respectively.
iv. Range
Steps of determining range value:
Step 1: Identification of highest value
Maximum value: 27
Step 2: Assessing smallest value from data set
Minimum value: 5
Step 3: Range value can be determined by subtracting smallest figure from the highest one
(Amrhein, Trafimow and Greenland, 2019)
Range: 27 – 5
= 22 km/hr
v. Standard deviation
Step 1: Calculating squares of wind speed value (X) which in turn denoted as X^2
Step 2: Now, calculating the sum of X^2

Step 3: Thereafter, ∑x^2 / N
Step 4: (∑x / n) ^ 2
Step 5: outcome of Step3 – step 4
Step 6: for determining SD Square of step 5 is calculated such as: SQRT 49.05
= 7 km/hr
Date
Km/h
(x) X^2
30-Sep 20 400
01-Oct 27 729
02-Oct 5 25
03-Oct 22 484
04-Oct 5 25
05-Oct 12 144
06-Oct 16 256
07-Oct 15 225
08-Oct 22 484
09-Oct 21 441
Total 165 3213
Standard deviation= Square root of ∑x^2 / N – (∑x / n) ^ 2
= SQRT of (3213 / 10) – (165 / 10) ^ 2
= SQRT of 321.3 – 272.25
= SQRT 49.05
= 7 km/hr
Outcome of SD shows that mean value of wind speed will deviate from 7 km/hr.
Hence, referring this figure weather department can do planning about near future.
4. Doing forecast by using linear method of statistics
i. Steps of calculating m value
Through following below mentioned steps value of m can be calculated
m = NΣxy – Σx Σy / NΣ x^2 – (Σx)^2
1. In the first stage Σxy is multiplied by n

2. Thereafter, multiplication of Σx* Σy with n will be done
3. At third stage, following formula is used
NΣxy – Σx Σy
4. NΣ x^2 – (Σx)^2 is done
5. Output of NΣxy – Σx Σy / NΣ x^2 – (Σx)^2

ii. Presenting the steps of calculating c
By undertaking following steps value of c can be determined:
1. Initialy, summation of Y (wind speed data) is determined
2. At this step, following formula is multiplied
M * ΣX
3. Thereafter, value of m * Σx is divided by n
4. For calculating value of c outcome of step 3 is subtracted from Σy
iii. Making wind speed forecast for day 14 and 21
Date X
Km/hr
(y) XY X^2
30-Sep 1 5 5 1
01-Oct 2 5 10 4
02-Oct 3 12 36 9
03-Oct 4 15 60 16
04-Oct 5 16 80 25
05-Oct 6 20 120 36
06-Oct 7 21 147 49
07-Oct 8 22 176 64
08-Oct 9 22 198 81
09-Oct 10 27 270 100
Total 55 165 1102 385
m = NΣxy – Σx Σy / NΣ x^2 – (Σx)^2
Y = mX + c
m = 10 (1102) - (55 * 165) / (10 * 385) – (55)^2
m = (11020 - 9075) / (3850 – 3025)
m = 1945 / 825
m = 2.36

c = Σy – m Σx / N
c = 165 – (2.36 * 55) / 10
c = (165 – 129.67) / 10
c = 35.33 / 10
c = 3.53
Forecasting wind speed
km/hr for day 14
Y = mX + c Here x = day 14
Y = 2.36 (14) + (3.53)
Y = 33 + 3.53
Y = 36.53 km/hr
Forecasting for day 21
Y = mX + c Here x = day 21
Y = 2.36 (21) + 3.53
Y = 49.51 + 3.53
Y = 53.04 km/hr
CONCLUSION
In conclusion to this report, it can be presented that fluctuating trend takes place in the
wind speed of Lewisham area. Further, it has been articulated that by taking into account
linear forecasting prediction about Lewisham wind speed can be done appropriately.

REFERENCES
Books and Journals
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.
Sclove, S. L., 2018. A course on statistics for finance. Chapman and Hall/CRC.
Online
Lewisham weather data. 2019. Online. Available through: <
https://www.worldweatheronline.com/lewisham-weather-history/lewisham-greater-
london/gb.aspx>