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Chart 1: Column chart of humidity for 10 days
(Source: self created)
Chart 2: Line chart of humidity for 10 days
(Source: self created)
Mean = Sum of all the observations / Number of total observations
= 98.1 + 98.6 + 99.2 + 90.3 + 86.5 + 95.3 + 92.9 + 96.3 + 94.3 + 95.1 / 10
= 946.6 / 10
In the above calculation, the mean of the collected data is determined. The humidity changes for 10 days have been collected for the calculation where the humidity of a city for day 1 is 98.1. While, the humidity of the city shifted to 98.6 on day 2 and 99.2 on day 3. However, on day 4 the humidity decreased to 90.3 and on another day it even decreased to 86.5 i.e. on day 5. On day 6 and 7 the humidity of the city was analyzed as 95.3 and 92.9. On day 8 the humidity of the city is determined as 96.3 while on day 9 the humidity is determined as 94.2. The humidity of the city is analyzed as 95.1 on day 10. Therefore the mean is calculated by summing up all the humidity changes of 10 days by the number of days which is 10 (Harahap et al. 2018). Therefore, the sum of all the data is computed as 946.6 and it is divided by the number of days which is 10 and the mean is computed as 94.66.
Data in ascending order
86.5, 90.3, 92.9, 94.2, 95.1, 95.3, 96.3, 98.1. 98.6 and 99.2
Median = (n / 2)th + (n / 2 + 1)th / 2
= (10 / 2) + (10 / 2 +1) / 2
= 5th + 6th / 2
= 95.1 + 95.3 / 2
= 190.4 / 2
In the above calculation, the median of the humidity for 10 days has been calculated. The median is basically called as the middle value in a set of numbers and data. If the set of numbers is odd, the middle number of the set is simply considered as the median of the set of numbers, while for computing the median in a set of even numbers a formula is used. The calculation is started by arranging them in ascending order starting from the lowest value of 86.5 and ending to the highest value of 99.2 (Zimmermann et al. 2020). The formula used for determining the median of the humidity changes is (n / 2)th + (n / 2 + 1)th / 2. By using this formula the 5th and 6th observation is analyzed which is 86.5 and 95.3. Then the average of these two data has been formed by summing up both and dividing the outcome by 2. The sum of these two data has been valued as 190.4 which is divided by 2 and gives the value of median as 95.2.
As the humidity of 10 days are distinctive from each other and the data are not repeated, there will be no mode in this case.
Range = highest observation - lowest observation
= 99.2 - 86.5
In the above calculation, the range of the set of numbers relating to the humidity changes in the city for 10 days has been determined. Range is basically considered as the difference between the lowest value of a number in a set of numbers and the highest value of it (Slob and Burgess, 2020). Here, the highest humidity value is 99.2 while the lowest value of humidity is 86.5. Therefore, a range of 12.7 has been calculated by deducting the lowest value of humidity 86.5 from the highest value of humidity which is 99.2.
X? (Mean) = 94.66
Standard deviation = √∑ (x - X?) ^ 2 / n - 1
= √(98.1 - 94.66)2 + (98.6 - 94.66)2 + (99.2 - 94.66)2 + (90.3 - 94.66)2 + (86.5 -
94.66)2 + (95.3 - 94.66)2 + (92.9 - 94.66)2 + (96.3 - 94.66)2 + (94.2 - 94.66)2 + (95.1 -
94.66)2 / 10 - 1
= √12.25 + 16 + 21.16 + (8.6) + (65.61) + (0.49) + 2.89 + (2.89) + (0.16) + 0.25 / 9
The above calculation is made to determine the standard deviation of the collected data of humidity changes of a city for 10 days. In order to compute the standard deviation, the mean has been computed using the humidity values of 10 days. Here the mean is calculated as 94.66 which is used in the formula √∑ (x - X?) ^ 2 / n - 1. Therefore, by putting all the data in the formula, the value of standard deviation has been formed as 3.94.
Using the linear model of forecasting, the value of m and c is required to be computed, where the variable x represents the days number while on the other side, the y variable represents the value of humidity for that particular day (Bose and Emirates, 2018). This value of humidity changed everyday using which the humidity for day 11 and day 13 is being forecasted. Here, the N represents the total number of days which is 10.
I Calculation of m value
m = ((N∑xy− ∑x∑y) / (N ∑ x2 −(∑x)2))
m = (((10 5177.9) - (55 946.5)) / ((10 * 385) - 3025))
m = ((51779 - 52057.5) / (3850 - 3025))
m = -278.5 / 825
m = -0.337
In the above calculation, the formula of N∑xy− ∑x∑y) / (N ∑ x2 −(∑x)2 is used to determine the value of m and it is determined as -0.337.
II. Calculation of c value
c = (∑y− m∑x) / N
c = (946.5 - (-0.337) * 55) / 10
c = (946.5 + 18.535) / 10
c = 965.035 / 10
c = 96.5035
In the above calculation, the formula of (∑y− m∑x) / N is used to determine the value of c and it is determined as 96.5035.
III. Forecasting Humidity
Humidity on day 11:
y = mx + c
y = ((-0.337) * 11) + 96.5035
y = -3.707 + 96.5035
y = 92.79
Here, by using the formula of mx + c, the humidity on day 11 is forecasted as 92.79.
Humidity on day 13:
y = mx + c
y = ((-0.337) * 13) + 96.5035
y = -4.901 + 96.5035
y = 91.60
In the above calculation, the forecasted humidity on day 13 is determined as 91.60 by using the formula mx + c.
Bose, I. and Emirates, U.A., 2018. Employee empowerment and employee performance: An empirical study on selected banks in UAE. Journal of Applied Management and Investments, 7(2), pp.71-82.
Harahap, A., Zuhriyah, A. and Rahmayanti, H., 2018. Relationship between knowledge of green product, social impact and perceived value with green purchase behavior. In E3S Web of Conferences (Vol. 74, p. 04002). EDP Sciences.
Kurniawan, D.A., Perdana, R. and Kurniasari, D., 2018. Identification of student attitudes toward physics learning at batanghari district high school. The Educational Review, USA, 2(9), pp.475-484.
Slob, E.A. and Burgess, S., 2020. A comparison of robust Mendelian randomization methods using summary data. Genetic epidemiology, 44(4), pp.313-329.
Zimmermann, M., Ender, A. and Mehl, A., 2020. Local accuracy of actual intraoral scanning systems for single-tooth preparations in vitro. The Journal of the American Dental Association, 151(2), pp.127-135.
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