Statistical Analysis of Parisian Weather: A 10-Day Study

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Data of the weather has been collected for the city Paris, France for ten consecutive days
from 10th January 2017 to 19th January 2017. Two parameters of the weather are considered,
namely humidity and temperature and these parameters are represented in % and °C
respectively. All the data is tabled down in the Excel sheet and the following operations are
performed. Data which is gathered is following:
Date
Temperature (°
C) Humidity (%)
10-Jan 8 85
11-Jan 10 90
12-Jan 6 89
13-Jan 4 86
14-Jan 4 88
15-Jan -1 97
16-Jan 1 100
17-Jan -1 86
18-Jan -2 75
19-Jan -1 72
The data can be represented visually in the form of charts and graphs. Two types of charts are
used to represent the data, namely bar graph and line chart.
Bar graph:
Figure 1: Data is represented in the form of bar graph
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Line chart:
Figure 2: Data represented in the form of line chart
Calculation of mean:
Mean is the average value of the data. It can be calculated by adding up the given data and
then dividing it by number of numbers given (Purplemath, 2019).
Mean = ∑ of numbers
number of numbers
Mean of temperature:
Mean = 8+10+6+4+4 ± 1+1± 1 ±2 ±1
10
Mean = 28
10
Mean = 2.8
So, the mean temperature is 2.8
Mean of humidity:
Mean = 85+90+ 89+ 86+88+ 97+100+86+ 75+72
10
2

Mean = 868
10
Mean = 86.8
So, the mean humidity is 86.8
Excel formula for calculating mean of temperature is =MEAN(B2:B11)
Excel formula for calculating mean of humidity is =MEAN(C2:C11)
Calculation of median:
Median refers to the mid-value of the given data. It is calculated by arranging the data in
ascending order and then finding the middle value (Zheng, et. al., 2017). If the elements in
the data are in odd number, then the middle value will be the answer and if the elements are
in even number, then the average of two mid-values will be the answer for the median.
Median of temperature:
Arrangement of data in ascending order: -2, -1, -1, -1, 1, 4, 4, 6, 8, 10
The elements are even in number; therefore the average of the mid values 1 and 4 is the
answer.
Median = 1+ 4
2
Median = 5
2
Median = 2.5
So, the answer for the median of temperature is 2.5
Median of humidity:
Ascending order arrangement: 72, 75, 85, 86, 86, 88, 89, 90, 97, 100
The elements of the data are even in number; therefore the average of two mid values will be
the answer. The mid values are 86 and 88.
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Median = 86+88
2
Median = 174
2
Median = 87
So, the median of humidity is 87.
Excel formula for calculating median of temperature is =MEDIAN(B2:B11)
Excel formula for calculating median of humidity is =MEDIAN(C2:C11)
Calculation of mode:
Mode is the value that is frequently occurring in the data. If no number in the data is
repeating, then there will be no mode value for the given data (Purplemath, 2019).
Mode of temperature:
Temperature (°
C)
Frequency
8 1
10 1
6 1
4 2
-1 3
1 1
-2 1
-1 is occurring more often in the data; hence the mode of the temperature is -1.
Mode of humidity:
Humidity (%) Frequency
85 1
90 1
4

89 1
86 2
88 1
97 1
100 1
75 1
72 1
86 is frequently occurring, therefore the mode of humidity is 86.
Excel formula for calculating mode of temperature is =MODE(B2:B11)
Excel formula for calculating mode of humidity is =MODE(C2:C11)
Calculation of Range:
Range is the value difference between the largest and the smallest value (Zheng, et. al.,
2017).
Range of temperature:
Range = Largest value of temp – smallest value of temp
Largest value of temp = 10
Smallest value of temp = -2
Range= 10 – (-2)
Range = 12
So, the range of temperature is 12.
Range of humidity:
Range= largest value of humidity – smallest value of humidity
Largest value of humidity = 100
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Smallest value of humidity = 72
Range = 100 – 72
Range = 28
So, the range of humidity is 28.
Excel formula for calculating range of temperature is =MAX(B2:B11) - =MIN(B2:B11)
Excel formula for calculating range of humidity is =MAX(C2:C11) - =MIN(C2:C11)
Calculation of standard deviation:
Standard deviation of data tells about the deviation of data from its mean value and it also
measures the spreading of numbers (revision maths, 20119). It is denoted by The Greek
alphabet called Sigma.
Standard deviation = ❑
√ ∑ ( x− x ) 2
n−1
Where x is number
X bar is mean
n is total number of numbers
Standard deviation of temperature:
x x−x ( x−x ) 2
8 5.2 27.04
10 7.2 51.84
6 3.2 10.24
4 1.2 1.44
4 1.2 1.44
-1 -3.8 14.44
1 -1.8 3.24
-1 -3.8 14.44
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-2 -4.8 23.04
-1 -3.8 14.44
Sum= 161.6
Standard deviation = √ 161.6
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Standard deviation = 4.23
So, the standard deviation of temperature is 4.23
Standard deviation of humidity:
x x−x ( x−x )2
85 -1.8 3.24
90 3.2 10.24
89 2.2 4.84
86 -0.8 0.64
88 1.2 1.44
97 10.2 104.04
100 13.2 174.24
86 -0.8 0.64
75 -11.8 139.24
72 -14.8 219.04
Sum=657.6
Standard deviation = √ 657.6
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Standard deviation = 8.54
So, the standard deviation of humidity is 8.54
Excel formula for calculating standard deviation of temperature is =STDEVA(B2:B11)
Excel formula for calculating standard deviation of humidity is =STDEVA(C2:C11)
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Linear equation
The linear equation of line can be written as y = mx + c
Where m is the slope and c is the intercept.
Calculation of m:
m = ∑ ( x−x ) ( y − y )
∑ ( x−x ) 2
Calculation of c:
c = y - m x
Calculation of m and c for temperature data:
X y x- x y- y (x- x)(y- y) (x- x)^2
1 8 -4.5 5.2 -23.4 20.25
2 10 -3.5 7.2 -25.2 12.25
3 6 -2.5 3.2 -8 6.25
4 4 -1.5 1.2 -1.8 2.25
5 4 -0.5 1.2 -0.6 0.25
6 -1 0.5 -3.8 -1.9 0.25
7 1 1.5 -1.8 -2.7 2.25
8 -1 2.5 -3.8 -9.5 6.25
9 -2 3.5 -4.8 -16.8 12.25
10 -1 4.5 -3.8 -17.1 20.25
x=5.5 y=2.8 Sum= -107 Sum= 82.5
m = −107
82.5
m = -1.29
c = 2.8 – (-1.29)5.5
c = 9.895
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Calculation of m and c for humidity:
x y x-x y- y (x-x)(y- y) (x-x)^2
1 85 -4.5 -1.8 8.1 20.25
2 90 -3.5 3.2 -11.2 12.25
3 89 -2.5 2.2 -5.5 6.25
4 86 -1.5 -0.8 1.2 2.25
5 88 -0.5 1.2 -0.6 0.25
6 97 0.5 10.2 5.1 0.25
7 100 1.5 13.2 19.8 2.25
8 86 2.5 -0.8 -2 6.25
9 75 3.5 -11.8 -41.3 12.25
10 72 4.5 -14.8 -66.6 20.25
x=5.5 y=86.8 Sum= -93 Sum= 82.5
m = √ −93
82.5
m = -1.12
c = 86.8 – (-1.12)5.5
c = 92.96
Weather at day 15:
Temperature:
y = -1.29(15) + 9.89
y = -9.46
Humidity:
y = -1.12(15) + 92.96
y = 76.16
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So, the temperature and humidity on day 15 are -9℃ and 76.16% respectively.
Weather at day 23:
Temperature:
y = -1.29(23) + 9.89
y = -19.78
Humidity:
y = -1.12(23) + 92.96
y = 67.2
So, the temperature and humidity on day 23 are -19 ℃ and 67.2% respectively.
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References
Zheng, S., Mogusu, E., Veeranki, S.P., Quinn, M. and Cao, Y., 2017. The relationship
between the mean, median, and mode with grouped data. Communications in Statistics-
Theory and Methods, 46(9), pp.4285-4295.
Purplemath, 2019. Mean, Median, Mode, and Range. [Online]. Purplemath. Available at:
https://www.purplemath.com/modules/meanmode.htm. [Accessed on 20th May 2019].
Revision maths, 2019. Standard deviation. [Online]. Revision maths. Available at:
https://revisionmaths.com/gcse-maths-revision/statistics-handling-data/standard-deviation.
[Accessed on 20th May 2019].
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