Numeracy and Data Analysis: Statistical Tools and Linear Forecasting Model

This report discusses the use of mathematics in daily life and how to analyse charts, read data, interpret and make decisions accordingly. It covers the calculation of different statistical tools and Linear Forecasting Model using the example of humidity data of Scotland for the past 10 days. The statistical tools discussed include mean, median, mode, range, and standard deviation. The report also explains how to frame the regression equation and calculate the value of m and c.

Numeracy and Data
Analysis

Table of Contents
INTRODUCTION...........................................................................................................................3
MAIN BODY...................................................................................................................................3
1. Arrangement of the table format........................................................................................3
2. Present the data in chart format..........................................................................................3
3. Discuss the following by framing the step – wise calculations. ........................................4
4. Using the linear forecasting model frame the regression equation and calculate the value of
m and c...................................................................................................................................6
CONCLUSION ...............................................................................................................................8
REFERENCES................................................................................................................................9

INTRODUCTION
Numeracy means how to use and apply mathematics in our daily life. It helps in analysing charts,
read data, interpret and make decision accordingly. In the following, data is related to past 10
days of Scotland. It shows calculation of different statistical tools and Linear Forecasting Model.
MAIN BODY
1. Arrangement of the table format.
Date humidity
05-01-22 81
06-01-22 89
07-01-22 96
08-01-22 88
09-01-22 81
10-01-22 100
11-01-22 83
12-01-22 86
13-01-22 86
14-01-22 76
Table 1: Humidity data of Scotland of past 10 days
2. Present the data in chart format.
Chart 1: States different humidity level on different dates.

Chart 2:
3. Discuss the following by framing the step – wise calculations.
Mean: - It is the average of all the observation. Mean is one the three averages of central
tendency. For example, following are the marks obtained by the student in a exam are as follows
60, 70 ,80 ,85 ,65 then the mean of the student is 72. (Dumuid and et.al., 2018)
Steps to calculate mean: -
Step 1: - Determine all the values given
Step 2: - Add all the values given
Step 3: - Count the total number observation
Step 4: - Divide the sum of observation to the total number of observations
Mean= Sum of Observation/Total Number of observations
Mean = 866 / 10
= 86.6
Median: - It is the value which is derived after arranging the data in
ascending/descending order. Then the middle term among the series is the median of the series.
(Verma, Pal and Kumar, 2019)
Steps to calculate median: -
Step 1: - First of all arrange the data in ascending order (smallest to largest number)

Step 2: - Then calculate the number of observations whether it is odd/even.
Step 3: - If it is Even, then the following formula should be used (N/2)
Step 4: - And if it is odd, then the following formula should be used ((N+1)/2)
Step 5: - The resulted outcome is the position of the median.
Median: - If 'n' is odd = (N+1) / 2
If 'n' is even = (N/2)
In the following case all the data are in %: -
81, 89, 96, 88, 81, 100, 83, 86, 86, 76
76, 81, 81, 83, 86, 86, 88, 89, 96, 100
Median= (N/2)
= 10/2
= 5
Mode: - Mode is the value which has incurred most number of times.
Steps to calculate Mode: -
Step 1: - Collect and organise the data given.
Step 2: - Find out the distinct values.
Step 3: - Count the Frequency of occurrence of the data.
Step 4: - Most occurred value is the Mode.
76, 81, 81, 83, 86, 86, 88, 89, 96, 100
From the above data it can be found that the most occurring value are 81 and 86. This type of
mode is known as Bimodal.
Range: - The difference between the highest value and the lowest value is known as
Range. If the range is small, it represents the central tendency and if the range is large then it
does not represent the central tendency. (Schmidt and Burghardt, 2018)
Steps to calculate Range: -
Step 1: - Arrange all the data available.
Step 2: - Then identify the highest and the lowest value.
Step 3: - Subtract the lowest value from the highest.
Step 4: - The value we get after the third step is the Range.
Range= Maximum Value – Minimum value
Range= 100 – 76

Range= 24
Date Humidity xi - μ (xi - μ)2
14-01-22 76 -3.3 10.89
05-01-22 81 1.7 2.89
09-01-22 81 1.7 2.89
11-01-22 83 3.7 13.69
12-01-22 86 6.7 44.89
13-01-22 86 6.7 44.89
08-01-22 88 8.7 75.69
06-01-22 89 9.7 94.09
07-01-22 96 16.7 278.89
10-01-22 100 20.7 428.49
Total 73 997.3
Standard Deviation: - It is the distance of the variable from the central tendency, which
is generally mean. (Lall, Thomas and Suhling,2018)
Steps to Calculate Standard Deviation
Step 1: - Firstly we have to find the mean of the data given.
Step 2: - For each observation find out the difference between the value and the mode of the
data.
Step 3: -Sum of all the values of step 2.
Step 4: - Divide by number of terms (n).
Step 5: - Finally, Square root the result of step 4.
Standard Deviation= √ (xi – μ) 2 / N
= √ (464.4) / 10
= √ 46.44
= 6.81
4. Using the linear forecasting model frame the regression equation and calculate the value of m
and c.
Linear Forecasting Model: - It predicts ' future values' based on the 'past values' in a linear
y = mx + c
where, 'y' is the dependent variable
'mx' is the independent variable
'c' is the constant
Steps of Calculating m is:

1. Multiply both the variables X and Y which are named as days and humidity.
2. Do the sum of the above calculation.
3. Sum of the x variable and y factor individually.
4. Then multiply both the factors.
5. Calculate ( x)⅀ 2 at the end put the values in the formula.
6. The resultant value is the value of 'm'.
S.no Date Humidity xi - μ (xi - μ)2
1 14-01-22 76 -10.6 112.36
2 05-01-22 81 -5.6 31.36
3 09-01-22 81 -5.6 31.36
4 11-01-22 83 -3.6 12.96
5 12-01-22 86 -0.6 0.36
6 13-01-22 86 -0.6 0.36
7 08-01-22 88 1.4 1.96
8 06-01-22 89 2.4 5.76
9 07-01-22 96 9.4 88.36
10 10-01-22 100 13.4 179.56
Total 5.68 464.4
m= 10 (4951) – (55) * (866) / 10 * (385) – (55) 2
m= 49510 – 47630 / 3850 - 3025
m= 1880 / 825
m= 2.28
Steps of calculation value of 'c'
1. First of all, calculate the sum of 'y' variable.
2. Then calculate the sum of 'x' variable.
3. Finally divide it with the sum of 'N'.
4. The value derived from Step 3 is the value of 'c'.

c= 866 – 2.28 * (55) / 10
c = (866 – 125.4) / 10
c = 74.06
Humidity on Day 11: -
m= 2.28, c= 74.06, x= 11,
y= mx + c
y= 2.28(11) + 74.06
y = 25.08 + 74.06
y = 99.14
Humidity on Day 13: -
m=2.28, c= 74.06, x=13
y= mx+ c
y= 2.28 (13) + 74.06
y= 29.64 + 74.06
y= 103.70
CONCLUSION
From the above mentioned report, Table 1. shows different humidity reported in last 10 days in
Scotland. Chart 1 and 2 shows that on 10/01/2022 the humidity was the highest. Different
statistical tool shows the following results after calculating the mean, median and mode are 86.6,
5 and 81/86 respectively. The Range and Standard deviation are 24 and 6.81 respectively. The
value of standard deviation states that the variable deviates more than the mean. The values of
'm' and 'c' derived from the linear forecasting model are 2.28 and 74.06 respectively. From the
following data it can be forecasted that On Day 11 and Day 13 the humilities are 99.14 and
103.70 respectively.

REFERENCES
Books and Journals
Dumuid, D. and et.al., 2018. Compositional data analysis for physical activity, sedentary time and sleep
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Verma, A. K., Pal, S. and Kumar, S., 2019. Classification of skin disease using ensemble data mining
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Lall, P., Thomas, T. and Suhling, J., 2018, May. Feature Extraction and RUL Prediction of SAC Solder
Alloy Packages by Different Statistical and Time-frequency Analysis Techniques under
Simultaneous Temperature-Vibration Loads. In 2018 17th IEEE Intersociety Conference on
Thermal and Thermomechanical Phenomena in Electronic Systems (ITherm) (pp. 1270-1279).
IEEE.
Schmidt, T. and Burghardt, M., 2018, August. An evaluation of lexicon-based sentiment analysis
techniques for the plays of gotthold ephraim lessing. Association for Computational Linguistics.
Yadav, S., Jain, A. and Singh, D., 2018, December. Early prediction of employee attrition using data
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