Data Analysis of Telephone Bills: Numeracy Homework Assignment

This assignment provides a comprehensive analysis of telephone bill data using various numeracy and data analysis techniques. The report begins with an introduction to data analysis and its significance, followed by the presentation of telephone bill data in both tabular and chart formats. The main body of the assignment involves the calculation of key statistical measures, including mean, mode, median, standard deviation, and range, to understand the central tendencies and variability of the data. Furthermore, the assignment utilizes a linear model to estimate future telephone bill values for the 12th and 14th days, demonstrating predictive analysis capabilities. The conclusion summarizes the findings and emphasizes the importance of data analysis in interpreting information from diverse sources. The assignment includes relevant references to support the analysis and methodologies employed.

Numeracy and data
analysis

Table of Contents
Table of Contents.............................................................................................................................2
INTRODUCTION...........................................................................................................................1
MAIN BODY..................................................................................................................................1
Representation of bill data in tabular format...............................................................................1
Representation of information in chart format............................................................................1
Calculation of mean, mode, median, standard deviation and range............................................2
Calculation of values of m, c and future estimation of bill with the help of linear model..........5
CONCLUSION................................................................................................................................6
REFERENCES................................................................................................................................7

INTRODUCTION
Data analysis can be defined as the process of analysing and assessing the information
which is gathered from different sources. With the help of it answers for all the questions that are
related to the topic researched are figured out. It is a technique which is beneficial to conduct
details analysis of collected data (Bebeau, 2019). Present report is based upon numeracy and data
analysis of 10 day’s information of telephone bills. For this purpose, the information is
represented in the form of table as well as chart. On the other hand, mean, mode, median,
standard deviation, range are calculated. Apart from this, linear model is also used so that details
of future could be analysed.
MAIN BODY
Representation of bill data in tabular format
The details that are mentioned in below table are related to electricity bill.
Particulars
Details
('00)
1 25
2 32
3 19
4 38
5 27
6 36
7 29
8 24
9 47
10 32
Representation of information in chart format
Line chart:
1

From the above chart it has been determined that the value of bill is fluctuating
during the selected time period. At the 9th day it was the highest and at 3rd day it was the
lowest.
Columns chart:
The above column chart is showing that the value of bill is changing during the period. It
also states that usage of telephone is changing continuously with the changes in time.
Calculation of mean, mode, median, standard deviation and range
Particulars
Details
('00)
2

1 25
2 32
3 19
4 38
5 27
6 36
7 29
8 24
9 47
10 32
Mean 30.9 or 31
Mode 32
Median 26.5
Standard
deviation 8.0339557
Max 47
Min 19
Range 28
Mean: It can be defined as the average value of data set which is collected from different
sources. While calculating it, the total values in series are divided with the total of data series.
Formula and steps for the calculation of it are as follows:
Formula = ∑X (Total of data series) / N (Total values in data series)
= 309 / 10
= 30.9 or 31
Mode: It could be described as the number which is repeating in the data series more
than one time. When there is no number which gets repeated in the data series then it will be
considered that there is no mean in the information.
From the data series of telephone bill, it has been analysed that the mode for the series is
32 because this number is repeated in the whole series (Bokhari, Rashid and Chan, 2016).
Median: It is the middle value or the number of data series. When the data series is even
then the results are calculated by adding 1 in the total values. If the data is odd then the total
number of values are divided by 2. As the data series of telephone bill is even therefore
following steps will be followed to calculate the median:
Formula: N (Total values in series) + 1 / 2
= 10 + 1 / 2
3

= 5.5th observation
= 27 + 26 / 2
= 26.5
Standard deviation: It can be defined as the statistical measure which is used for the
purpose of determining the diffusion in the data series (Exley and Trimble-Roles, 2016). In order
to calculate it different values are required to be analysed which are calculated in following
table:
Particulars Details
(x) x-m (x-m)2
1 25 -5.9 34.81
2 32 1.1 1.21
3 19 -11.9 141.61
4 38 7.1 50.41
5 27 -3.9 15.21
6 36 5.1 26.01
7 29 -1.9 3.61
8 24 -6.9 47.61
9 47 16.1 259.21
10 32 1.1 1.21
Total 580.9
Formula to calculate standard deviation: √ (variance)
Formula to calculate Variance = {∑ (x – mean) 2 / N}
= 580.9 / 10
= 58.09 or 58(Variance)
Standard deviation = √58
= 7.61 Standard deviation
4

Range: Difference between lower and upper value of data series is known as range. In
order to calculate it maximum and minimum values of services are required to be assessed
(Hodges, 2019). The steps for its calculations are as follows:
= MAX – MIN
= 47 – 19
= 28
Calculation of values of m, c and future estimation of bill with the help of linear model
In order to estimate the value of telephone bill for 12th and 14th day following steps are
followed in linear model:
1. Table:
Particulars
(x)
Details
('00) (y) X2 ∑xy
1 25 1 25
2 32 4 128
3 19 9 171
4 38 16 608
5 27 25 675
6 36 36 1296
7 29 49 1421
8 24 64 1536
9 47 81 3807
10 32 100 3200
∑x= 55 ∑y= 309 ∑x2=385 ∑xy = 12867
2. Calculating value of M
Formula for calculating the of M: M= N ∑ xy - ∑x*∑y / N ∑x2 - (∑x)2
= 10 * 12867 – (55 * 309) / 10 * 385 - (55)2
= 128670 – 16995 / 3580 - 3025
= 111675 / 825
= 135.36 or 135
3. Calculating Value of c:
Formula: ∑y - m ∑x / N
5

= (309 – 135 * 55) /10
= 309 - 7425 / 10
= -7116 / 10
= -711.6 or 712
4. Telephone bill at day 12: Y= mx + c
Y= 135 * 12 + (-712)
= 908
5. Telephone bill at day 14: Y= mx + c
Y= 135 * 14 + (-712)
= 1178
CONCLUSION
From the above project report, it has been concluded that data analysis is a technique
which is followed by researchers for the purpose of interpretation the information which is
gathered by them from different sources. There are various elements of it which are calculated to
find best results. These are mean, mode, median, standard deviation and range. Linear model is
also used in it to forecast future expenses.
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REFERENCES
Books and Journals:
Bebeau, C. M., 2019. Graphicacy for Numeracy: Review of Fundamentals of Data Visualization:
A Primer on Making Informative and Compelling Figures by Claus O. Wilke
(2019). Numeracy: Advancing Education in Quantitative Literacy. 12(2).
Bokhari, R., Rashid, S. M. and Chan, S. H., 2016. Teachers’ Perception on the Implementation
of the Literacy, Numeracy and Screening (LINUS LBI 2.0) Programme among Lower
Primary ESL Pupils. Malaysian Journal of ELT Research. 11(1). p.14.
Exley, B. and Trimble-Roles, R., 2016. Written numeracy assessment in the early years: The
challenges of pronouns and noun groups. Australasian Journal of Early Childhood.
41(1). pp.100-105.
Hodges, B., 2019. On Numeracy and Pricing (Doctoral dissertation).
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