Numeracy and Data Analysis : Solved Assignment

Numeracy and Data Analysis

Table of Contents
INTRODUCTION ...................................................................................................................................3
MAIN BODY...........................................................................................................................................3
1. Arranging data in a table format......................................................................................................3
2. Presentation......................................................................................................................................4
3. Steps for calculating the values of following methods....................................................................5
4. Forecasting of station usage for 12 and 15 years.............................................................................7
1. Steps for calculating m value..........................................................................................................7
2. Steps for calculating c value...........................................................................................................7
CONCLUSION........................................................................................................................................9
REFERENCES.........................................................................................................................................9

INTRODUCTION
Statistics has been defined as one of the most important term for every business organisation. Data
gathered by company has to be analysed and interpreted in the correct manner. Analysis of numerical
data should be done with the help of best and suitable statistical tools. Interpretation of data after
being analysed is done for better understanding about information and for making smooth decision.
The present report is based on Chingford, UK train station usage made by passengers for last 10 years
ranging from year 2009 to 2018. Also, it will define about various steps of statistical tools such as
mean, median, mode etc. which has to be followed for analysis data. Data will be presented with the
help of graph along with interpretation. At last, the report will discuss about forecasting factor and
process related to calculating the values of 'm' and 'c' in the linear forecasting model.
MAIN BODY
1. Arranging data in a table format
Year Total usage of Train
Station (in 000)
2009-10 11
2010-11 16
2011-12 19
2012-13 151
2013-14 147
2014-15 161
2015-16 178
2016-17 19
2017-18 42
2018-19 650
Interpretation – From the above table it can be interpreted that over the period of ten years,
passengers has started using Chingford train station either in form of entry or exit from the station.
The usage of train station is showing increasing trend during last 10 year time period. In the year 2009
– 10, it is lowest with value of 11. On the other hand, in 2018 – 2019 passengers has made use of
station maximum i.e. 650.
2. Presentation
Column Chart – It is a method of presenting data in the graphical form. The data in Column chart is
presented by displaying vertical bars displaying horizontally across the chart having values axis given

on the left side of the chart graph.
Line Chart – Also known as Line plot or Line graph. It displays figures or information in the form of
series of data points connected with the help of straight line segments.
Interpretation – With the help of above graph, it has been evaluated that Chingford train
station has been used by the passengers at maximum times in the year 2018 – 2019 with value 650.
During the time period of 10 years, the minimum train usage is done in year 2009 – 2010 by
passengers in form of entry and exit.
3. Steps for calculating the values of following methods.
1. Mean - First select all the data values of either small or large size of which average has to be
2009-10
2010-11
2011-12
2012-13
2013-14
2014-15
2015-16
2016-17
2017-18
2018-19
0
100
200
300
400
500
600
700
11 16 19
151 147 161 178
19 42
650
Total usage of Train Station
(in 000)
2009-10
2010-11
2011-12
2012-13
2013-14
2014-15
2015-16
2016-17
2017-18
2018-19
0
100
200
300
400
500
600
700
11 16 19
151 147 161 178
19 42
650
Total usage of Train Station
(in 000)

find. Add up together all the values for further calculation (George and Mallery, 2016). Count
the number of values given in question and then divide it by sum of set by the number of
values.
Year Total usage of train
station (x)
2009-10 11
2010-11 16
2011-12 19
2012-13 151
2013-14 147
2014-15 161
2015-16 178
2016-17 19
2017-18 42
2018-19 650
Total (∑X) 1394
Mean = ∑X ÷ N
N = 10
∑X = 1394 / 10
= 182.7
2. Median - The data in the given data set should be first arrange in order from the least to the greatest
form. If the given data set is having any even number of items, then it will be considered as the
median by taking the average of the two middle number or value in data set.
Firstly arranging data set in an ascending order
Year Train usage data set
1 11
2 16
3 19
4 19
5 42
6 147
7 151
8 161
9 178
10 650
Median = (N + 1) / 2

= (10 + 1)/2
= 11 / 2
= 5.5 item
In this case:
(Value of 5th item + value of 6th item) / 2
= (42 + 147) / 2
Median = 94.5
3. Mode - Arrange all the data set in the described form as per the requirement of question. Give order
to the number ranging from the small to large as per their degree (Luo and et.al., 2018). Count the
number of times each number is repeating or recurring. At last, identify the value or number which is
repeating or occurring the most will be mode value.
Mode = NA
4. Range - Arrange all the data set in either the highest or lowest sequence form. Then calculate the
highest and lowest numbers in the given data set. Subtract the smallest number identified in the data
set from the largest number. This is the range value.
Maximum value = 650
Minimum value is dataset = 11
Range = maximum – minimum value
Range = 650 - 11
Range = 639
5. Standard deviation - First calculate simple mean of given data set. After that, for each number
subtract it from mean obtained and square the value obtain. Calculate the mean of the squared
differences. Square root the value achieved.
Year Total usage of train
station (X) X^2
2009-10 11 121
2010-11 16 256
2011-12 19 361
2012-13 151 22801
2013-14 147 21609
2014-15 161 25921
2015-16 178 31684
2016-17 19 361
2017-18 42 1764

2018-19 650 422500
Total 1394 527378
Standard deviation= SQRT of ∑x^2 / N – (∑x/n)^2
= SQRT of (422500 / 10) – (1394 / 10) ^ 2
= SQRT 42250 – 19432.36
= SQRT of 22817.64
Standard deviation = 151.06
4. Forecasting of station usage for 12 and 15 years.
1. Steps for calculating m value.
For determining the value of m, formula used is m = NΣxy – Σx Σy / NΣ x^2 – (Σx)^2. Steps are as
follows:
1. Calculate the total value of X and Y by adding together on individual basis.
2. Now, multiply the value of X and Y so as to obtain the value of XY.
3. Add the value of XY to determine the summation value of XY
4. Calculate the square value of X and makes addition of it.
5. Put all the values ascertained in the formula m = NΣxy – Σx Σy / NΣ x^2 – (Σx)^2 to derive
the value of m.
2. Steps for calculating c value.
The value of c is determined with the help of formula c = σy - mσx / n. steps to be followed are as
followed:
1. Calculate the total value of Y.
2. Multiply the total value of X with value of m obtained.
3. Put all the values in formula so as to determine the value of c.
3. Forecasting for 12 and 15 years.
Forecasting is a method of making estimation or prediction about the future happening. With
the help of budget, forecasting can be done about revenue and expenses to be incurred related to
carrying own a business operation. In this report, forecasting has been done about train station usage
for a time period of 12 and 15 years
Year
Number
of year
(X)
Total usage
of train
station (Y)
XY X^2

2009-10 1 11 11 1
2010-11 2 16 32 4
2011-12 3 19 57 9
2012-13 4 151 604 16
2013-14 5 147 735 25
2014-15 6 161 966 36
2015-16 7 178 1246 49
2016-17 8 19 152 64
2017-18 9 42 378 81
2018-19 10 650 6500 100
Total 55 1394 10681 385
Particulars Formula Y = mX + c
m
m = NΣxy – Σx Σy / NΣ x^2 –
(Σx)^2
m = 10 (10681) - (55 * 1394) /
(10 * 385) – (55)^2
m = (106810 - 76670) / (3850 –
3025)
m = 30140 / 825
m = 36.53
c c = Σy - mΣx / N
c = 1394 – (36.53 * 55) / 10
c = (1394 – 2009.33) / 10
c = -615.33/10
c = -61.53
Forecasting station
usage for 12 year
Y = mX + c Here x = 12 Years
Y = 36.53 (12) + (-61.53)
Y = 438.36 – 61.53
Y = 376.83
Forecasting for 15
year
Y = mX + c Here x = 15 Years
Y = 36.53 (15) + (-61.53)
Y = 547.95 – 61.53
Y = 486.42
CONCLUSION
From the above report it can be concluded that analysis of data helps company in preparation
of financial statements. By using right statistical tool, a company can determine the meaningful value
of data and thus can make interpretation accordingly. The report has defined about train station usage
made by the passengers of Chingford in form of entries and exits made. The report has defined that in
the year 2009 – 2010 it is lowers with value of passengers as 11. Whereas, the passengers has made

use of Chingford train station maximum with value of 650 in the year 2018 – 2019. It can be assessed
that within a period of ten consecutive years, usage of Chingford train station has increased.
REFERENCES
Books and Journals
George, D. and Mallery, P., 2016. Descriptive statistics. In IBM SPSS Statistics 23 Step by Step (pp.
126-134). Routledge.
Luo, D. and et.al., 2018. Optimally estimating the sample mean from the sample size, median, mid-
range, and/or mid-quartile range. Statistical methods in medical research. 27(6). pp.1785-1805.
Madichie, N. O. and Fiberesima, O., 2019. Management education trends and gaps–A case study of a
community education provision in London (UK). The International Journal of Management
Education.
Rees, D. G., 2018. Essential statistics. Chapman and Hall/CRC.
Online
Steps to calculate mean. 2019. [Online]. Available through: <https://www.wikihow.com/Calculate-
the-Mean>.