Numeracy and Data Analysis: Measures of Central Tendency, Linear Forecasting Model

This report by Desklib covers the humidity level of Liverpool, UK in table and chart form, measures of central tendency and dispersion with their steps, and the application of a linear forecasting model to find humidity levels on day 11 and day 13. The report concludes that using tools such as mean, mode, and median can help organizations make decisions regarding profitability and performance.

and Data Analysis
( Pass Criteria )

Contents
INTRODUCTION...........................................................................................................................2
MAIN BODY...................................................................................................................................2
1. Presentation of humidity level of Liverpool,UK in table format.......................................2
2. Representation of humidity level day wise data in chart form...........................................3
3.Computing values of measures of central tendency,range and standard deviation with their
steps........................................................................................................................................4
4.Application of Linear forecasting model.............................................................................5
a. calculation of m value with steps........................................................................................5
b. Determining c value and its procedure...............................................................................6
c. Finding day 11 and day 13 humidity level by using formula.............................................7
CONCLUSION................................................................................................................................7
REFERENCES................................................................................................................................8
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INTRODUCTION
Data analysis refers to the process of interpreting useful information for decision making
process in the organisation. This report contains four sections, in section one there is a tabular
representation of humidity level of Liverpool, UK of last ten days. Section 2 include charts and
pie chart of humidity level. In section three, there is a brief description about central tendency
measures and dispersion measures while mentioning their steps. Last section consists calculation
of m and c values and interpreting day 11 and day 13 with the use of linear forecasting model.
MAIN BODY
1. Presentation of humidity level of Liverpool,UK in table format
Day
Humidity
level
1 94
2 95
3 90
4 95
5 92
6 75
7 95
8 89
9 82
10 81
Table 1: This table is showing humidity level of Liverpool of last 10 days
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2. Representation of humidity level day wise data in chart form
Graph 1: Line graph showing humidity level on different days
Graph 2: Column Chart representing level of humidity.
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3.Computing values of measures of central tendency,range and standard deviation with their
steps
 Mean- It can be find out by adding all the series and dividing with sum of observations in
a data. This is a measure of central tendency and used in further statistical test used in
statistics (Alizadeh, et.al., 2020.). Steps for finding mean values are as follows-
Step-1: Add all the given numbers.
Step-2: Count the number of observations present in a given data.
Step-3: Divide the sum calculated in step-1 by number of observations.
Series- 94, 95 ,90 ,95 ,92 ,75 ,95 ,89 ,82, 81
Formula for mean-
= Sum of observations / Number of observations
= 888/10
= 88.8
 Median- It can be found out by ordering the series from ascending to descending order.
This is another measure of central tendency and also known as mid value. If number of
observation are even, average the two mid numbers but in case of odd numbers directly
middle value will be the median (Clarizia ,et.al.,2019). Procedure for calculating median-
Step-1: Sort the data in lowest to highest form.
Step-2: If data is even average the centre value in given numbers.
Step-3: Number of observations are odd then middle value will be the median.
Sequencing events in sorted format-
75, 81, 82 , 89, 90, 92 , 94 , 95, 95 , 95
Formula for median-
5th term + 6th term / 2
= 90 + 92 / 2
= 91
 Mode- It can be defined as the most occurring or common values in the series. This is
also known as fashionable value because it is most frequent term in the data. When there
is a single mode it is known as Bimodal and having more than two mode it is called
multimodal (Wallace ,et.al.,2019). Steps for calculating mode are as follows-
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Series-75, 81, 82, 89, 90, 92, 94, 95, 95, 95
Step-1: Use inspection method to observe mode
Step-2: Select the numbers which is occurring most frequently
Step-3: From the above data it can be interpreted that 95 will be the answer
Hence, Mode will be 95.
 Range- It is a measure of dispersion and takes the most two extreme values in the data.
This is calculated by taking the difference between highest value and the lowest value
given in the humidity level of Liverpool.
Method to compute are described as follows-
Step-1: Filter the numbers in ascending to descending order (Zhang, et.al.,, 2019).
Step-2: Subtract the lowest value in range from the highest value.
Data- 75, 81, 82 , 89, 90, 92 , 94 , 95, 95 , 95
Range= Highest value- lowest value
=95-75
=20
 Standard deviation- In statistics it shows the amount of variation in the data. This a
dispersion measure. Lower the deviation, better it shows the reliability between sample
and population mean (Zheng, Lu, and Lantz, 2018). Steps for estimating SD are as
follows-
Step-1-Find mean of the humidity level of the Liverpool.
Step-2: Deduct mean from humidity level.
Step-3: Square the value calculated in step-2.
Step-4: Divide the step 3 by number of days.
SD = √ (xi – μ) 2 / N
= 21.25 / 10
=2.125
4.Application of Linear forecasting model
a. calculation of m value with steps
Step-1: Firstly, find product of x and y and multiply with n.
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Step-2: Find product of sum of x and y values.
Step-3: Deduct step 2 from step 1.
Step-4: Multiply square of x with n and subtract from square of x.
Step-5: Divide step-3 by step-4
x= Total of days
y=Humidity level
n= Number of observations
= 10* 4769 – 55 * 888 / 10 * 385 / 10 * 55 – 385
= 47690- 48840 / 550 – 385
= - 1150 / 165
= - 6.96
b. Determining c value and its procedure
Step-1: Find the sum of y.
Step-2: Multiply m value with sum of x
Step-3: Divide step 2 by n.
= 888 - (- 6.96 ) 55 / 10
= 127.08
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c. Finding day 11 and day 13 humidity level by using formula
Equation- Day 11:
y = mx + c
= ( -6.96) 11 + 127.08
= -76.56 + 127.08
= 50.52
Day 13-
y= mx + c
= (-6.96) 13 +127.08
= - 90.48 + 127.08
= 36.6
CONCLUSION
From the above report it can be concluded that using tools such as mean, mode and median any
organisation is capable to take decision regarding profitability and performance of an enterprise.
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REFERENCES
Books and Journals
Alizadeh, R., et.al., 2020. Performance evaluation of complex electricity generation systems: A
dynamic network-based data envelopment analysis approach. Energy Economics, 91.
p.104894.
Clarizia, M.P.,et.al.,2019. Analysis of CYGNSS data for soil moisture retrieval. IEEE Journal of
Selected Topics in Applied Earth Observations and Remote Sensing, 12(7),.pp.2227-
2235.
Wallace, L.M.,et.al.,2019. Investigation of frailty as a moderator of the relationship between
neuropathology and dementia in Alzheimer's disease: a cross-sectional analysis of data
from the Rush Memory and Aging Project. The Lancet Neurology, 18(2). pp.177-184.
Zhang, L., et.al.,, 2019. Bioinformatics analysis of metagenomics data of biogas-producing
microbial communities in anaerobic digesters: A review. Renewable and Sustainable
Energy Reviews, 100. pp.110-12
Zheng, Z., Lu, P. and Lantz, B., 2018. Commercial truck crash injury severity analysis using
gradient boosting data mining model. Journal of safety research, 65. pp.115-124.
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