Numeracy and Data Analysis: Arrangement, Presentation, Calculation, Forecasting

This study material from Desklib covers the topics of arranging data in tables, presenting data through charts, calculating mean, median, mode, range, and standard deviation, and using linear forecasting model for future temperature in Liverpool. It includes step-by-step calculations and explanations, along with examples and references from relevant books and journals.

Numeracy and Data Analysis

Table of Contents
MAIN BODY..................................................................................................................................3
1.Arrangement of data in table format.........................................................................................3
2. Presenting the data through charts...........................................................................................3
3. Steps for the calculation and highlighting the final value.......................................................4
4. Using linear forecasting model and forecasting the humidity of future days..........................8
REFERENCES................................................................................................................................1

MAIN BODY
Collecting humidity of Liverpool for 10 consecutive days
Temperature from 12th September to 21th March 2022 with respect to Liverpool is as follows -
94, 88, 88, 72, 77, 82, 59, 94, 94, 82
1.Arrangement of data in table format
Serial. No. Date Humidity of Liverpool for
the ten consecutive days (in
%)
1 12th September 2022 94
2 13th September 2022 88
3 14th September 2022 88
4 15th September 2022 72
5 16th September 2022 77
6 17th September 2022 82
7 18th September 2022 59
8 19th September 2022 94
9 20th September 2022 94
10 21st September 2022 82
N = 10 ∑X 830
2. Presenting the data through charts
Line Chart -

Clustered Column Chart –
3. Steps for the calculation and highlighting the final value
Mean – It refers to the average of a set of values. The mean is calculated by totalling up the
value of all the observation and dividing the resulting sum with the number of observation in the
data set (Hosoyama, Maeda and Saiki, 2021). Mean is therefore, the single value which helps in
representing the entire data set. The symbol of mean is addressed as x bar indicated as x̄.

Formula for mean = x̄ = ∑X / n
∑X = 94+88+88+72+77+82+59+94+94+82 = 830
n = 10
x̄ = 830 / 10 = 83
Median – It is referred as the middle value which is represented in the data set and can be
obtained through arranging the data in ascending or descending order. The median value is
where the values which are 50% and are both above and below it (Satman, 2022).
There is description of data set which contains even number of observations and along
with this the median can be analysed with the help of totalling the two numbers which are lying
in the middle and are divided by the same number by 2.
Median for the data set with the temperature of ten consecutive days is –
Serial No. Temperature data arranged in
ascending order
1 59
2 72
3 77
4 82
5 82
6 88
7 88
8 94
9 94
10 94
This is the data set which consist of even number of observations which are 10 and there are two
numbers which are identified in the middle which are 82 and 88. Thus, when adding the values
together and dividing the resulting sum by two, it will provide the median for the data.

Median = 82 + 88 / 2 = 170 / 2 = 85.
Mode – It is the value which appears most in the data set. The modal value is also defined which
has been occurred within the data set. The mode of the data which has been identified is 82.
And this concerns the temperature of Liverpool city as it is the most frequent data series which is
appearing.
Range – Range is defined as the basic measure of dispersion which is performed under the data
set. There is range which can be achieved by subtracting the lowest value from the highest value
which is identified within the data set (Šrámek, Široký and Hlavsová, 2018). There is highest
value in the temperature data which is observed as 94 and the lowest value which is identified is
59. Therefore, the range of this data set is 94 – 59 = 35.
Standard deviation – Standard deviation is defined as the statistics that measures the dispersion
of the data set while calculating the mean as it is helping to calculate the square root of the
variance. There is the description of the small value of standard deviation which helps in
indicating the mean value and this represents the data set in appropriate manner.
There are certain steps which help in determining the standard deviation and this is as
follows –
 There is proper analysis and calculation of the mean value for the data set.
 In the further process, there is subtraction of the mean value from all the values which are
individual within the series and then squaring the result (El Omda and Sergent, 2021).
 There is summation of the square value and then dividing it with the number of
observations.
 There is placement of the results which are obtained in the third step under the square
root which helps in providing the standard deviation from the data set which has been
framed.
Formula - σ =

Serial.
No. Date Temperature
of Liverpool X- Mean (x- mean)^2
1 12th September 2022 94 11 121
2 13th September 2022 88 5 25
3 14th September 2022 88 5 25
4 15th September 2022 72 -11 121
5 16th September 2022 77 -6 36
6 17th September 2022 82 -1 1
7 18th September 2022 59 -24 576
8 19th September 2022 94 11 121
9 20th September 2022 94 11 121
10 21st September 2022 82 -1 1
Mean 83 1148
σ = √ 1148 / 10 = 114.8

4. Using linear forecasting model and forecasting the humidity of future days
Linear forecasting model - y = mx + c
Serial. No.
X
Temperature of
Liverpool Y
xy x2
1 94 94 1
2 88 176 4
3 88 264 9
4 72 288 16
5 77 385 25
6 82 492 36
7 59 413 49
8 94 752 64
9 94 846 81
10 82 820 100
55 830 4530 385
I. Calculating of the value of m
m =
m = (10 * 4530) – (55 *830) / (10 * 385) – (55)2
m = 45300 – 45650 / 3850 – 3025
m = 350 / 825 = 0.42
m indicates that the linear model is steep. This indicates the regression line’s direction
II. Calculation of the value of c

c =
c = 830 – (0.42 * 55) / 10
c = 830 – 23.1 / 10
c = 806.9/ 10 = 80.69
C is defined as the constant value of the linear forecasting model and this shows the distance
which is stated between the starting between point origin and y – axis.
III. Forecasting Temperature for 11th and 12th day
x = 11th day
y = mx +c
y = 0.4 * 11 + 80.69
y = 4.4 + 80.69 = 85.09
x = 12th day
y = 0.4 * 14 + 80.69
y = 5.6 + 80.69 = 86.29
Result Statement - Therefore, temperature in Liverpool on 11th & 12th day would be
85.09 and 86.29 respectively.

REFERENCES
Books and Journals
El Omda, S. and Sergent, S.R., 2021. Standard deviation.
Hosoyama, K., Maeda, K. and Saiki, Y., 2021. What does complete revascularization mean in
2021?–Definitions, implications, and biases. Current opinion in
cardiology. 36(6). pp.748-754.
Satman, M.H., 2022. Teaching the median with terms of absolute value, differentiability, and
optimization. Alphanumeric Journal. 10(1). pp.41-50.
Šrámek, P., Široký, J. and Hlavsová, P., 2018. Capacity range–definition and calculation.
In MATEC Web of Conferences. Vol. 235. EDP Sciences.
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