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Question :
Learning Outcomes
- Analyse and use techniques for summarising and evaluating data.
- Present reasonableness in the calculation of answers.
- Discuss and examine techniques used for forecasting.
Project Brief:
You are required to disseminate humidity data for ten consecutive days from any city of your choice. This data can be easily collected using online sources. Once you have gather the humidity data for ten days, you are required to produce a report undertake the following:
- Arrange the data in a table format.
- Present the data using any two types of charts of your choice. Example: Column Chart, scatter plot, pictograms.
- Calculate and demonstrate the following: Analyse the following values to examine final values:
- Mean
- Median
- Mode
- Range
- Standard Deviation
4. With the help of data, use the linear forecasting model which is y = mx + c to calculate and demonstrate the followings:
- Show the steps of calculation of m
- Show the steps of calculation of cvalue and discuss the answer.
- By using the calculated 'm' and 'c' values, forecast the humidity for day 15 and day 20.
Introduction
What this assignment is about?
Calculation and discussion of the mean, mode, median, range, standard deviation and the forecasting.
Arranging the humidity data in a table
|
Day Number |
Humidity % |
|
1 |
91 |
|
2 |
96 |
|
3 |
90 |
|
4 |
93 |
|
5 |
83 |
|
6 |
90 |
|
7 |
87 |
|
8 |
82 |
|
9 |
85 |
|
10 |
81 |
Developing a line chart for the humidity data
Creating a column chart for the humidity data
Calculation and discussion of the mean
µ=
µ = Mean
∑ = Sum of / Total
x = Individual data value
N = Number of items
µ==
µ=87.8%
Calculation and discussion of the median
81, 82, 83, 85, 87, 90, 90, 91, 93, 96
Median Position =
Median Position = =
Median Position = 5.5
81, 82, 83, 85, 87, 90, 90, 91, 93, 96
Median= = 88.5%
Calculation and discussion of the mode
In this case, there is only only one mode, which is 90 % has been repeated two times during the ten days period.
Calculation and discussion of the range
Range – difference between highest and lowest value.
The range = Highest humidity – Lowest humidity
Range = 96 – 81
Range = 15%
Calculation and discussion of the standard deviation
σ =
σ = Standard deviation
µ = Mean
∑ = Sum of / Total
x = Individual data value
N = Number of items
|
N |
x |
|
x-y |
( |
|
1 |
91 |
87.8 |
3.2 |
10.24 |
|
2 |
96 |
87.8 |
8.2 |
67.24 |
|
3 |
90 |
87.8 |
2.2 |
4.84 |
|
4 |
93 |
87.8 |
5.2 |
27.04 |
|
5 |
83 |
87.8 |
- 4.8 |
23.04 |
|
6 |
90 |
87.8 |
2.2 |
4.84 |
|
7 |
87 |
87.8 |
- 0.8 |
0.64 |
|
8 |
82 |
87.8 |
- 5.8 |
33.64 |
|
9 |
85 |
87.8 |
- 2.8 |
7.84 |
|
10 |
81 |
87.8 |
- 6.8 |
46.24 |
µ = 87.8% ∑ = 225.6
σ = = =
σ = 4.74%
Calculation and discussion of the ‘m’ value
m =
∑ = Sum of / Total
x = Independent variable
y = Dependent variable
N = Number of items
|
x |
y |
|
xy |
|
1 |
91 |
1 |
91 |
|
2 |
96 |
4 |
192 |
|
3 |
90 |
9 |
270 |
|
4 |
93 |
16 |
372 |
|
5 |
83 |
25 |
415 |
|
6 |
90 |
36 |
540 |
|
7 |
87 |
49 |
609 |
|
8 |
82 |
64 |
656 |
|
9 |
85 |
81 |
765 |
|
10 |
81 |
100 |
810 |
|
∑x = 55 |
∑y = 878 |
∑ = 385 |
∑xy = 4720 |
m = = = =
m = -1.32%
Calculation and discussion of the ‘c’ value
c =
∑ = Sum of / Total
x = Independent variable
y = Dependent variable
N = Number of items
c = = = =
c = 95.06%
Forecast the humidity for day 15
y = mx+c
y = -1.32 x 15 + 95.06
y = -19.8 + 95.06
y = 75.26 % - humidity for day 15
Forecast the humidity for day 20
y = mx + c
y = -1.32 x 20 + 95.06
y = -26.4 + 95.06
y = 68.66% - humidity for day 20
Answer :
INTRODUCTION
Data analysis is the process of collecting and analysing data or information that helps in business operations to improve their performances or make future stargates (Kahan and et.al., 2017). This assessment based on humidity level of London and in this report required to represent data in line or column chart formal. In addition it includes the calculation of median, mode, mean, linear forecasting for future humidity forecasting etc.
MAIN BODY
1. Arrangement of data in tabular format
|
Days |
Humidity |
|
1 |
91 |
|
2 |
96 |
|
3 |
90 |
|
4 |
93 |
|
5 |
83 |
|
6 |
90 |
|
7 |
87 |
|
8 |
82 |
|
9 |
85 |
|
10 |
81 |
2. Representation of data in the chart format
Column Chart:
Line Chart:
Above mention charts represent the increasing or decreasing trend in the humidity in 10 continuous days (Kus, 2018). The first day humidity was 91 and and at the end of 10 days period it was 81. It represent the fluctuation in the humidity.
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3. Calculation the range of statistical value
|
Days |
Humidity |
|
1 |
91 |
|
2 |
96 |
|
3 |
90 |
|
4 |
93 |
|
5 |
83 |
|
6 |
90 |
|
7 |
87 |
|
8 |
82 |
|
9 |
85 |
|
10 |
81 |
|
Total |
878 |
|
Mean |
87.800 |
|
Mode |
89 & 90 |
|
Median |
86 |
|
Range |
15 |
|
Maximum |
96 |
|
Minimum |
81 |
|
Standard deviation |
4.74 |
Mean: It can be defined as the process where average of any of the data is calculated. For the purpose of finding the means, it is necessary that all of the given number must be added in the beginning and then in second particular stage, it becomes important that after add all of the given number it must be divided by the number of data available to find exact mean amount.
Formula - ∑X/N
= 878 / 10
= 87.8
Median: In mathematical term, median can be defined as the process of determining the average of a group of number. For the purpose of doing the calculation of median it is necessary to observe the value in smallest to largest. If the value is in odd number then the median will be of middle number and if it is not in odd number then average to middle two terms will be required to obtain.
Formula – [N+1] / 2
= [ 10 + 1 ] / 2
= 5.5th observation that is 87 & 90.
= 88.5
Mode: It is defined as the mathematical calculation where value is decided on the basis of frequent occurrence or even the value which is used for maximum times. The major advantage of mode is that it can be used in any type of given data but on the other hand of side, it is never possible in case of mean and median.
In this case, there is only one mode, which is 90 and it is repeating two times in 10 days (MalloyÂWeir and Cooper, 2017).
Range: It is explained as the process where difference between the highest and lowest value is required to be obtained (Range, 2018). The main advantage in range is it is very easy to do calculation in it and on the other hand the main cons in it is one of the sensitive to outlines where it doest give focus o n all of the available observations.
Formula = Maximum Value – Minimum Value
= 96 - 81
= 15
Standard deviation: In simple words, it can be defined as the measurement of dispersement in any of the statical terms. It gives the ideas about the data which has been spread out. It is calculated as on the basis of square root of variance where it is needed to determine the variation among each data which is related to mean.
|
Days |
Humidity (x) |
x- mean |
(x-m)2 |
|
1 |
91 |
3.2 |
10.24 |
|
2 |
96 |
8.2 |
67.24 |
|
3 |
90 |
2.2 |
4.84 |
|
4 |
93 |
5.2 |
27.04 |
|
5 |
83 |
-4.8 |
23.04 |
|
6 |
90 |
2.2 |
4.84 |
|
7 |
87 |
-0.8 |
0.64 |
|
8 |
82 |
-5.8 |
33.64 |
|
9 |
85 |
-2.8 |
7.84 |
|
10 |
81 |
-6.8 |
46.24 |
|
225.6 |
Formula = √Variance
Formula of Variance = [ ∑ (x–mean)2/N ]
= 225.6 / 10
= 22.56
Standard deviation = √ 22.56
= 4.74
4. Apply linear forecasting model and calculate y = mx = c
Forecasting can be defined as the process where it is needed to understand that predicition is required to be done on the basis of past and present data or performance. It is mainly helpful to find out the result before starting any of the project. Applying liner forecasting model and X will be consider as days and Y is humidity (Mendez-Carbajo, Jefferson and Stierholz, 2019). Further calculation mentioned below:
Step 1: Table formulation
|
Days (X) |
Humidity (Y) |
X2 |
XY |
|
1 |
91 |
1 |
91 |
|
2 |
96 |
4 |
192 |
|
3 |
90 |
9 |
270 |
|
4 |
93 |
16 |
372 |
|
5 |
83 |
25 |
415 |
|
6 |
90 |
36 |
540 |
|
7 |
87 |
49 |
609 |
|
8 |
82 |
64 |
656 |
|
9 |
85 |
81 |
765 |
|
10 |
81 |
100 |
810 |
|
∑x= 55 |
∑y= 878 |
∑X2= 385 |
∑XY= 4720 |
Step 2: Calculation of the value of M:
Formula: M = [N ∑XY - ∑x ∑y]/ [N ∑X2 - (∑x)2]
= [ 10 * 4720 – (55 * 878) ] / [10*385- (55)2 ]
= [47200 – 48290] / [3850 – 3025]
= -1090 / 825
= -1.32
Step 3: Calculation of value of C:
Formula = { ∑y - m ∑x } / N
= {878 – (-1.32 * 55)} / 10
= 950.6 / 10
= 95.06
Step 4: Humidity on 15th day:
Formula = Y = mx + c
= -1.32 * 15 + 95.06
= -19.8 + 95.06
= 75.26
The level of humidity on 15th day will be 75.26.
Step 5: Humidity on 20th Day:
Formula = Y = mx + c
= -1.32 * 20 + 95.06
= -26.4 + 95.06
= 68.66
The humidity level on 20th day will be 68.66.
CONCLUSION
From the above discussion it has been conclusion that data analysis use to gather information and use it in appropriate way. These information further beneficial for the future forecasting. With the help of statistical analysis, individual able to forecast the humidity for the future.
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