Numeracy and Data Analysis: Wind Speed Forecasting for London

This report presents a comprehensive analysis of wind speed data collected over ten days in London, UK. It begins by organizing the data in tabular form and visualizing it using column and line charts. The report then computes descriptive statistics, including mean, median, mode, range, and standard deviation, providing a detailed explanation of each calculation step. Furthermore, it employs a linear forecasting model to develop a regression equation, determining the values of 'm' (slope) and 'c' (intercept). The report also calculates the predicted wind speeds for the 11th and 13th days based on the derived linear model. The analysis includes all the steps and formulas used, offering a clear understanding of the data analysis and forecasting process.

NUMERACY AND
DATA ANALYSIS
Table of Contents

INTRODUCTION.......................................................................................................................3
TASK........................................................................................................................................3
1. Sort the information in a tabular form...........................................................................................3
2. Present above collected information with the help of charts.........................................................4
3. Compute the following by describing all the steps related to calculations.....................................4
4. With the help of linear forecasting model frame the regression equate and compute the value of
m and c..............................................................................................................................................7
a) Calculate value of m by explaining the required steps in the process.............................................7
b) Compute the value of c by stating down the steps which are included in calculation....................8
c) Ascertain the value of m and c for 11th and 13th day....................................................................8
CONCLUSION...........................................................................................................................9
REFERENCES...................................................................................................................................10

INTRODUCTION
Data analysis is helpful for collecting detailed data which would help to have an idea
about what is being done. The data in report is collected for city of London which is located in
UK. It has also included carrying out of descriptive statistics which is performed on data. Further
it has also calculated regression equation which would be formed and forecast of 2 days will be
made on basis of equation.
TASK
1. Sort the information in a tabular form.
Day
Wind
Speed
1 9
2 5
3 16
4 19
5 11
6 16
7 25
8 27
9 30
10 32
Total 190

2. Present above collected information with the help of charts.
The above prepared chart is the column chart which reflects the level of windspeed for 10
consecutive days.
The above developed chart is in the form of line chart which presents the windspeed on
every day basis which plots the wind speed level on a daily basis making a trend line.
3. Compute the following by describing all the steps related to calculations.
 Mean: It can be explained as average number related to value for which
information is being put at one place. In the above information the average
result of wind speed is computed for 10 consecutive days.
Steps involved in computation of mean:
Step 1: Find all the elements given.
Step 2: Sum all the values provided.

Step 3: Tally the summation of observation with total number of observations.
Mean = Summation of observations/Total number of observations
Mean =
 Median: It can be explained as a value which had been derived with the help
of sorting of data in ascending order. It is the middle element in the series
prepared and is denoted as median.
Steps for computing Median:
Step 1: At first place sort all the collected data and information in ascending order.
Step 2: After that compute the number of observations to know if it is odd or even.
Step 3: If the series results to be even then apply formula (n/2).
Step 4: If it results to be off then the following formula must be applied such as
(n+1/2).
Step 5: The result which was recorded is known as median.
Median = (n+1)/2
= (10+1) / 2
= 11/2 = 5.5
9, 5, 16, 19, 11, 16, 25, 27, 30, 32.
5, 9, 11, 16, 16, 19, 25, 27, 30, 32.
So, the median is calculated as (16+19) / 2 = 25.5
 Mode: It is the element or value which is noticed to take place most of the
time in a dataset.
Steps for calculating mode:
Step1: Collect and sort the information which is given.
Step2: Find which is distinct value.
Step 3: Tally the frequency of most occurring value from data set.
Step 4: Most occurring value observed is Mode.
9, 5, 16, 19, 11, 16, 25, 27, 30, 32.
It is thus observed from the above data set that the value which seems to get
repeated most of the time is 39. It has been repeated for 4 times.
 Range:

Steps for computation of Range:
Step 1: Arrange all the information available.
Step 2: Find out which one is the highest and lowest value.
Step 3: Subtract the lowest digit from the highest one.
Step 4: The value which is received after the step 3 is range.
Range = Maximum value - Minimum value
Range = 32 – 5 = 27.
 Standard deviation:
Steps involved in computation of Standard deviation
Step 1: At first find the mean of given data set.
Step 2: For every observation find the deviation between the value and the
mode of data.
Step 3: Add all values from Step 2.
Step 4: Divide it by number of terms (n).
Step 5: At last, square root the result observed in Step 4.
Standard deviation = √ (xi – μ) 2 / N
= √ (768) / 10
= √ 76.8
= 8.76
Day
Wind
Speed xi - μ (xi - μ)2
1 9 -10 100
2 5 -14 196
3 16 -3 9
4 19 0 0
5 11 -8 64
6 16 -3 9
7 25 6 36
8 27 8 64
9 30 11 121
10 32 13 169
Total 190 0 768

4. With the help of linear forecasting model frame the regression equate and compute the value
of m and c.
Linear forecasting model: It helps in predicting 'future results' that are based on 'past
values' in a linear equation formed.
y = mx + c
Where 'y' is stated as dependent variable
'mx' is the independent variable
'c' is the constant
a) Calculate value of m by explaining the required steps in the process.
Steps involved in computation of m is:
1. Multiply both the elements X and Y which are denoted as wind and speed.
2. Figuring out the sum of above computation.
3. Addition of x element and y element on a individual basis.
4. Afterwards multiply both the counted factors.
5. Calculate (x)2 and in the end place all the values in formula.
6. The resulted value will be the outcome of 'm'.
Day
Wind
Speed xy (x)2 (y)2
1 9 9 1 81
2 5 10 4 25
3 16 48 9 256
4 19 76 16 361
5 11 55 25 121
6 16 96 36 256
7 25 175 49 625
8 27 216 64 729
9 30 270 81 900
10 32 320 100 1024
Total 55 190 1275 385 4378

M = 10* 1275 – 1275 / 10* 385 – 385
= 12750 – 1275 / 3850 – 385
= 11475 / 3465
= 3.311
The above value of m depicts the slope of line that is 3.311.
b) Compute the value of c by stating down the steps which are included in calculation.
Steps for computation of c:
1. At first compute the sum of 'y' variable.
2. After that calculate the sum of 'x' element.
3. Then divide it by the sum of 'N'.
4. The value which would result from step 3 is the value of 'c'.
C = 190 – 3.311 * 55 / 10
= 7.895 / 10
= 0.785
c) Ascertain the value of m and c for 11th and 13th day.
Windspeed on Day 11:
M = 3.31, c = .785, x = 11
Y = mx + c
Y = (3.31 * 11) + .785
Y = 36.41 + .785
Y = 37.195
Windspeed on Day 13:
M = 3.31, c = .785, x = 13
Y = mx + c
Y = (3.31 * 13) + .785
Y = 43.03 + .785
y = 43.815

CONCLUSION
From the above calculated data, it can be asserted that the information of Wind speed
level is evaluated with the help of Mean, median, mode, range and standard deviation as well.
Further the regression equation was developed with the help of linear forecasting model.

REFERENCES
Books and Journals