Numeracy and Data Analysis: Descriptive Statistics and Linear Forecasting Model

This report discusses the use of mathematical strategies in daily life and the collection of data on humidity in Scotland. It covers the calculation of mean, median, mode, range, and standard deviation. It also explains how to compute the value of m and c using the linear forecasting model. The report provides insights into the daily climate of Scotland.

Numeracy and Data
Analysis

Table of Contents
INTRODUCTION...........................................................................................................................3
MAIN BODY...................................................................................................................................3
1. Organization of the table presentation................................................................................3
2. Set the information in a graphical form..............................................................................3
3. Calculate the descriptive statistics and show the steps.......................................................4
4. Compute the value of m and c by using the linear forecasting model...............................6
CONCLUSION................................................................................................................................8
REFERENCES................................................................................................................................9

INTRODUCTION
Numeracy can be defined as the use of mathematical strategies which is useful is the daily
lifestyle of an individual. In this report, the data of the city Scotland in collected which is based
in UK. On the basis of this different charts are being prepared. Accordingly, the mean, median
and the mode is computed along with the calculation of the range and standard deviation.
Further, the value of m and c is computation with the help of linear regression model.
MAIN BODY
1. Organization of the table presentation.
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
2. Set the information in a graphical form.

3. Calculate the descriptive statistics and show the steps.
Mean: - It is termed as the average of all the data which has been collected of the city. It
is evaluated by finding out the averages of the data (Dumuid and et.al., 2018).
Stages to determine mean: -
1. To collect the data of the country.
2. By doing the sum of all the figures.
3. Now to find the data collected of the number of days.
4. Now by dividing the sum and the total days.
Mean = Sum of humidity / Total Number of days
Mean = 866 / 10
= 86.6
Median: - It can be determined by the arranging of the data in the smallest to largest and
largest to smallest order. It is the mid value of the series which has been arranged (Verma, Pal
and Kumar, 2019).
Paces to analyse median: -
1. Sort the data in the ascending order.
2. Then, analyses that the data is of even or odd.
3. If the number of the data collected is even, then the formula used will be (N / 2)

4. If the data is odd that the formula will by (N + 1) / 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.
Stepladders to determine Mode: -
1. Gather and systematise the statistics known.
2. Discover the dissimilar values.
3. Sum the Occurrence of amount of the data.
4. Maximum happened value is the Mode.
76, 81, 81, 83, 86, 86, 88, 89, 96, 100
From the data calculation performed above it can be extracted that the most number of
times the value which has occurred is 81 and 86. This is known as Bimodal.
Range: - The variance between the uppermost and the lowermost value is recognized as
Range. If it is small, it characterises the central tendency and if it is great then it does not
embody the central tendency (Schmidt and Burghardt, 2018).
Paces to estimate Range: -
Step 1: - Organize the whole figures existing.
Step 2: - Now classify the peak and the bottommost value.
Step 3: - Deduct the bottom value from the maximum.
Step 4: - The value which 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: - This represents the value deviation from the mean of the data
which is collected (Lall, Thomas and Suhling, 2018).
Steps to estimate Standard Deviation
Step 1: - Firstly the mean of the data is evaluated.
Step 2: - Then the change from of each data value is deducted from the means.
Step 3: -Sum of all the values of step 2.
Step 4: - Divide by total observations.
Step 5: - At last, the square root
Standard Deviation= √ (xi – μ) 2 / N
= √ (464.4) / 10
= √ 46.44
= 6.81
4. Compute the value of m and c by using the linear forecasting model.
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 report prepared above, it can be summed up that the data of the city Scotland is
collected of the variable humidity. That information gathered is to find out the descriptive
statistics of the whole functional data and how the climate of the city varies daily. Further, in the
report, using the regression model, future humidity of 2 different days is calculated.

REFERENCES
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Solder Alloy Packages by Different Statistical and Time-frequency Analysis
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Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic
Systems (ITherm) (pp. 1270-1279). IEEE.
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