Statistical Analysis of Wind Speed Data

The provided assignment involves a statistical analysis of wind speed data in Leeds over ten consecutive days. The data includes wind speeds at different times, and the assignment requires calculating the mean, median, mode, and range of these values. Additionally, a forecast is made for wind speed after 14 and 21 days using linear regression. The results are presented in tables and interpreted to provide future wind speed predictions.

Numeracy and Data Analysis

Table of Contents
INTRODUCTION................................................................................................................................3
MAIN BODY.......................................................................................................................................3
1. Arrangement of data set in table format.......................................................................................3
2. Presentation of data......................................................................................................................3
3. Calculation...................................................................................................................................4
4. Forecasting of data.......................................................................................................................7
CONCLUSION....................................................................................................................................9
REFERENCES...................................................................................................................................10

INTRODUCTION
Data analysis is related with the process of evaluating and interpretation of given data set with the
help of statistical as well as mathematical tools and methods. By analysing data, better
understanding can be made about a particular phenomenon. The present report is on Leeds city,
United Kingdom. It will present data related to wind speed of past ten consecutive days with the
help of excels and graphs.
MAIN BODY
1. Arrangement of data set in table format.
Day Date Wind speed Km/h
1 28/09/19 13.29
2 29/09/19 10.45
3 30/09/19 12.03
4 01/10/19 7.57
5 02/10/19 8.34
6 03/10/19 9.6
7 04/10/19 11.34
8 05/10/19 11.24
9 06/10/19 11.04
10 07/10/19 11
Interpretation – From the above table it can be interpreted that the city of Leeds is facing
mix trend of wind speed in the past ten consecutive days I.e. From 28 September 2019 to 07
October 2019. Highest speed of wind was 13.29 km/h on 28 September with lowest wind speed of
7.57 km/h on 01 October (Crowder, 2017). Fluctuating trend has been noticed within a period of 10
days in Leeds.
2. Presentation of data.
1. Column Chart

2. Bar Chart
3. Calculation
Particulars Values
Mean 10.59
Median 11.02
Mode #NA
Range 5.72
Standard Deviation 1.6964603673
28/09/2019 30/09/2019 02/10/2019 04/10/2019 06/10/2019
0
2
4
6
8
10
12
14
Wind speed Km/h
28/09/2019
29/09/2019
30/09/2019
01/10/2019
02/10/2019
03/10/2019
04/10/2019
05/10/2019
06/10/2019
07/10/2019
0 2 4 6 8 10 12 14
Wind speed Km/h

1. Mean – Can be calculated by adding all the values of data set and taking average of it. The
mean value is obtained by summing all numbers and dividing it by total numbers of
observation (Edjabou and et.al., 2017).
Date Wind speed Km/h
28/09/19 13.29
29/09/19 10.45
30/09/19 12.03
01/10/19 7.57
02/10/19 8.34
03/10/19 9.6
04/10/19 11.34
05/10/19 11.24
06/10/19 11.04
07/10/19 11
N = 10
Total (∑X) 105.9
Mean
∑X ÷ N
105.9 / 10
= 10.59
2. Median – All numbers should be arrange in ascending order first. Determine the number of
observation is odd or even. In case of even item, median is calculated by taking average of
two middle numbers of the data set. And in case of odd, the median value will be centre
value of data set.
Date Wind speed Km/h
28/09/19 7.57
29/09/19 8.34
30/09/19 9.6
01/10/19 10.45
02/10/19 11
03/10/19 11.04
04/10/19 11.24
05/10/19 11.34

06/10/19 12.03
07/10/19 13.29
Median
(N + 1) / 2
= (10 + 1)/2
= 11 / 2
= 5.5 item
Median
(Value of 5th item +
value of 6th item) / 2 =
(11 +11.04) / 2 = 11.02
3. Mode – Arrange every numbers from smallest to largest (Little and Rubin, 2019). Do
counting of number of times the number is repeating. The value which is repeating the most
is mode value.
Particulars Wind speed (in
km/h)
Mode #NA
The mode value is determined by arranging all the given values of data set as per their order.
The number which is having the highest frequency or which is repeating most often is considered as
the mode value of that data set. Therefore, in this case no number is repeating as a result of which
mode value is not available.
4. Range – Determine the maximum and minimum value of the data set. For calculating the
value of range, subtract minimum value from the maximum value determined.
Particulars Figures
Maximum wind
speed 13.29
Minimum wind
speed 7.57
Range =
Maximum –
Minimum value
5.72

5. Standard Deviation – First calculate, mean of data set given and then subtract each number
from mean determined. Squaring the value obtained after such subtraction and calculating
again mean value of squared difference. Finally taking square root for ascertaining standard
deviation value.
Date Wind Speed
km/h X^2
28/09/19 13.29 176.6241
29/09/19 10.45 109.2025
30/09/19 12.03 144.7209
01/10/19 7.57 57.3049
02/10/19 8.34 69.5556
03/10/19 9.6 92.16
04/10/19 11.34 128.5956
05/10/19 11.24 126.3376
06/10/19 11.04 121.8816
07/10/19 11 121
Total 105.9 1147.3828
Standard deviation= SQRT of ∑x^2 / N – (∑x / n) ^ 2
= SQRT of (1147.3828 / 10) – (105.9/ 10) ^ 2
= SQRT of 114.73828 – 112.1481
= SQRT of = 2.59018
= 1.609403616
4. Forecasting of data.
1. Steps for calculating value of m.
For calculating m value, formula is m = N Σxy – Σx Σy / N Σ x^2 – (Σx)^2.
Steps are as follows:
 Determine the value of x and y variables by summing up on individual basis i.e. Σx Σy.
 Multiply value of x and y to obtain Σxy and then multiply it with the total number of
observation (Ozay and Celiktas, 2016).

 Subtract step 1 from step 2.
 Calculate square root of individual x variable and add it up for evaluating Σ x^2 after that
multiply it with the total number of observation.
 Take square root of Σx.
 Subtract value of step 5 from step 4.
 Divide final values obtained from step 3 and step 6.
2. Steps for determining c value.
Formula for evaluating value of c = Σy - mΣx / N.
Steps includes:
 Add all the values of y and x variable for obtaining Σy and Σx.
 Multiply Σx with m value determined and divide it with the total number of observation.
 Subtract step 2 from step 1 for identifying value of c (Varmuza and Filzmoser, 2016).
3. Forecasting of wind speed for 14 and 21 days.
Date Number of days (X) Total wind
speed (Y) XY X^2
28/09/19 1 13.29 13.29 1
29/09/19 2 10.45 20.9 4
30/09/19 3 12.03 36.09 9
01/10/19 4 7.57 30.28 16
02/10/19 5 8.34 41.7 25
03/10/19 6 9.6 57.6 36
04/10/19 7 11.34 79.38 49
05/10/19 8 11.24 89.92 64
06/10/19 9 11.04 99.36 81
07/10/19 10 11 110 100
Total 55 105.9 578.52 385
Particulars Formula Y = mX + c
m NΣxy – Σx Σy / NΣ x^2 – (Σx)^2 M = 10 (578.52) - (55 * 105.9) / (10 *

385) – (55)^2
m = ( 5785.2 – 5824.5) / (3850 –
3025)
m = −39.3 / 825
m = −0.047636364
c Σy - mΣx / N
c = 105.9 – (−0.047636364 * 55) / 10
c = ( 105.9 –(−2.62000002)) / 10
c = 108.520000025 / 10
c = 10.852000002
Forecasting
wind speed
for 14 days
Y = mX + c Here x = 14 days
Y = −0.0476363647 (14) +
10.852000002
Y = −0.666909106 + 10.852000002
Y = 10.185090896
Forecasting
wind speed
for 21 days
Y = mX + c
Here x = 21 days
Y = −0.047636364 (21) +
10.852000002
Y = −1.000363644 + 10.852000002
Y = 9.851636358

Interpretation – It can be interpreted that wind speed of Leeds after 14 days will be
10.185090896 km/h. And after 21 days the speed of wind will decrease to 9.851636358 km/h.
CONCLUSION
From the above report it can be concluded that the city of Leeds is having fluctuating trend
in its wind speed data set studied of past ten consecutive days. Forecasting has been done for 14 and
21 days which determines wind speed of 10.185090896 km/h and 9.851636358 km/h.

REFERENCES
Books and Journals
Crowder, M. J., 2017. Statistical analysis of reliability data. Routledge.
Edjabou, M. E. and et.al., 2017. Statistical analysis of solid waste composition data: Arithmetic
mean, standard deviation and correlation coefficients. Waste management. 69. pp.13-23.
Little, R. J. and Rubin, D. B., 2019. Statistical analysis with missing data (Vol. 793). John Wiley &
Sons.
Ozay, C. and Celiktas, M. S., 2016. Statistical analysis of wind speed using two-parameter Weibull
distribution in Alaçatı region. Energy Conversion and Management. 121. pp.49-54.
Varmuza, K. and Filzmoser, P., 2016. Introduction to multivariate statistical analysis in
chemometrics. CRC press.
Online
Mean, median, mode and Range analysis. 2019. [Online]. Available through:
<https://www.purplemath.com/modules/meanmode.htm>.