Numeracy and Data Analysis Report: Sofia Bulgaria Humidity Analysis

This report presents a detailed analysis of humidity data for Sofia, Bulgaria, over a 10-day period, incorporating various statistical techniques. The analysis begins with data presented in tabular and graphical formats, including line and column charts for visual representation. Descriptive statistics are then computed, including mean, median, mode, range, and standard deviation, providing insights into the central tendency and dispersion of the humidity data. Furthermore, the report employs a linear forecasting model to predict humidity values for the 15th and 20th days, offering future projections based on the established data trends. The report concludes with a comprehensive overview of the methodologies and findings, supported by relevant references.

Numeracy and Data Analysis

Table of Contents
1. data in the table form ..............................................................................................................3
2. Graph .......................................................................................................................................3
2. computing descriptive value by application of statistical techniques .....................................4
4. Calculating humidity value for 15th and 20th day by using the linear forecasting model .....7
REFERENCES................................................................................................................................1

The present report is based on the humidity analysis of Sofia Bulgaria for the 10
consecutive days with an application of statistical techniques. Furthermore, forecasting model is
used for making prediction of the humidity in the coming days.
1. data in the table form
Days Date Humidity data (%)
1 03/12/19 76
2 04/12/19 93
3 05/12/19 87
4 06/12/19 75
5 07/12/19 87
6 08/12/19 71
7 09/12/19 71
8 10/12/19 76
9 11/12/19 93
10 12/12/19 93
2. Graph
Line chart

Column graph
03/12/2019
04/12/2019
05/12/2019
06/12/2019
07/12/2019
08/12/2019
09/12/2019
10/12/2019
11/12/2019
12/12/2019
0
10
20
30
40
50
60
70
80
90
100
Humidity data (%)

2. computing descriptive value by application of statistical techniques
a. value of Mean
Days Date Humidity data (%)
1 03/12/19 76
2 04/12/19 93
3 05/12/19 87
4 06/12/19 75
5 07/12/19 87
6 08/12/19 71
7 09/12/19 71
8 10/12/19 76
9 11/12/19 93
10 12/12/19 93
Sum of the humidity data 822
Total number of the
observation 10
Mean value (%) 82.2
03/12/2019
04/12/2019
05/12/2019
06/12/2019
07/12/2019
08/12/2019
09/12/2019
10/12/2019
11/12/2019
12/12/2019
0
10
20
30
40
50
60
70
80
90
100
76
93
87
75
87
71 71
76
93 93
Humidity data (%)

Interpretation- The above figures interprets that humidity data of the 10 consecutive days
of Sofia Bulgaria represents the mean value as 82.2 % or 0.82 (George and Mallery, 2016). This
reflects that the average value of the humidity in Sofia attained as 82.2%. It is been expressed by
dividing the total of the humidity data accounted as 822 with that of the total observation that
equates to 10.
b. value of median
Step 1- Ascending order data
Days Date Humidity data (%)
1 08/12/19 71
2 09/12/19 71
3 06/12/19 75
4 03/12/19 76
5 10/12/19 76
6 05/12/19 87
7 07/12/19 87
8 04/12/19 93
9 11/12/19 93
10 12/12/19 93
Step 2
Number of observation
Median (n+1)/2
(10+1)/2
5.5
Median value (0.76+0.87)/2
0.815
Median 81.50%

Interpretation- The median value from the humidity dataset of Sofia Bulgaria is seen as
81.50% for the 10 days. This value is called as the mid-value of the data which means that the
value that separates higher half with that of the lower half from the data sample. The steps that
need to be followed for computing median value is arranging the data in an ascending form and
then employing the formula reflected as (n+1)/2 for computing the median observation. The
resulted observation equating to 5.5 so the average is taken of the 5th and the 6th observation that
is (76%+87%)/2 in order to get accurate median value.
c. Mode
Days Date Humidity data (%)
1 03/12/19 76
2 04/12/19 93
3 05/12/19 87
4 06/12/19 75
5 07/12/19 87
6 08/12/19 71
7 09/12/19 71
8 10/12/19 76
9 11/12/19 93
10 12/12/19 93
Mode or modal value 93
Interpretation- The above results depicts the modal value of Sofia Bulgaria Humidity
data as 93% or 0.93. It is defined as the value which occurs on a frequent basis within the set of
an observation (McCarthy and et.al., 2019). It is determined by way of counting the number of
the time every value comes into the dataset.
d. Range
Range
Largest value 93.00%
Smallest value 71.00%

range value 93%-71% 0.22
22.00%
Interpretation- Range reflects the amount of the dispersion that is present in the data that
evaluated as 22%. It is computed by subtracting the smallest value or minimum value as 71%
from largest or the maximum value as 93% (Bonner, 2018). As the resulted range value of
humidity data is 0.22, a larger range which in turn indicates a greater dispersion within the
dataset.
e. Standard deviation
Date Humidity data (%)(X) X^2
03/12/19 0.76 0.58
04/12/19 0.93 0.86
05/12/19 0.87 0.76
06/12/19 0.75 0.56
07/12/19 0.87 0.76
08/12/19 0.71 0.50
09/12/19 0.71 0.50
10/12/19 0.76 0.58
11/12/19 0.93 0.86
12/12/19 0.93 0.86
Total 8.22 6.83
Standard deviation= Square root of ∑x^2 / N – (∑x / n) ^ 2
= SQRT of (6.83 / 10) – (8.22 / 10) ^ 2
= SQRT of (.683 – .675684)
= SQRT of 0.0084
= 0.092
Interpretation- From the above table, it has been analysed that the standard deviation
resulted as 0.092 which is counted as the measure of an average distance in between the dataset
values and mean (Young and Wessnitzer, 2016). It is computed by the evaluating Square root of

the value that is accounted applying the formula. As the value is low so it means data point seen
as very much close to mean.
4. Calculating humidity value for 15th and 20th day by using the linear forecasting model
Date Days (x)
Humidity data
(%)(Y) X*Y X^2
03/12/19 1 0.76 0.76 1
04/12/19 2 0.93 1.86 4
05/12/19 3 0.87 2.61 9
06/12/19 4 0.75 3 16
07/12/19 5 0.87 4.35 25
08/12/19 6 0.71 4.26 36
09/12/19 7 0.71 4.97 49
10/12/19 8 0.76 6.08 64
11/12/19 9 0.93 8.37 81
12/12/19 10 0.93 9.3 100
Total 55 8.22 45.56 385
m = NΣxy – Σx Σy / NΣ x^2 – (Σx)^2
Y = mX + c
m = 10 (45.56) - (55 * 8.22) / (10 * 385) – (55)^2
m = (455.6 – 452.1) / (3850 – 3025)
m = 3.5 / 825
m = 0.004 or 0.42%
c = Σy – m Σx / N
c = 8.22 – (0.004 * 55) / 10
c = (8.22 – .22) / 10
c = 8 / 10
c = 0.8
computing value of Y by making use of m and c value
For 15 days-

Y = mX + c
= 0.004(15)+0.8
= 0.15+0.83
= 0.86 or 86%
For 20 days -
Y = mX + c
= 0.004(20)+0.8
= 0.08+0.8
= 0.88 or 88%
Interpretation- The above evaluation shows the forecast of the humidity data for the 15th
and the 20th day of the Sofia Bulgaria resulted as 86% and 88% (Humidity data of Sofia
Bulgaria, 2018). It is calculated by using the model known as linear forecasting where the value
of m & c is computed by following the formula equated as 0.004 & 0.8 and the these values were
putted in the equation that is Y= mX+c.

REFERENCES
Books and journals
Bonner, M. D., 2018. Descriptive statistics. Police Abuse in Contemporary Democracies. p.257.
George, D. and Mallery, P., 2016. Descriptive statistics. In IBM SPSS Statistics 23 Step by
Step (pp. 126-134). Routledge.
McCarthy, R. V. and et.al., 2019. What Do Descriptive Statistics Tell Us. In Applying Predictive
Analytics (pp. 57-87). Springer, Cham.
Young, J. and Wessnitzer, J., 2016. Descriptive statistics, graphs, and visualisation. In Modern
statistical methods for HCI (pp. 37-56). Springer, Cham.
Online
Humidity data of Sofia Bulgaria. 2018. [Online]. Available through: <https://weather-and-
climate.com/average-monthly-Humidity-perc,govedartsi-sofia-bg,Bulgaria>
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