DAT0001B Using Numeracy, Data and IT: Assessment Part 2

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DAT0001B
Using Numeracy, Data and IT
Assessment Part 2
Student name:
Student id:
0

Contents
Executive Summary.........................................................................................................................3
a) Total, Mean, Median and Standard Deviation.........................................................................5
b) Graphical summary..................................................................................................................8
c) Scatter diagram..........................................................................................................................11
d) Probability.................................................................................................................................12
References......................................................................................................................................14
List of figures
Figure 1 Total, mean, median, standard deviation...........................................................................6
Figure 3 Food...................................................................................................................................8
Figure 4 Clothing.............................................................................................................................8
Figure 5 Entertainment....................................................................................................................9
Figure 6 Charitable Giving..............................................................................................................9
Figure 7 Summarization................................................................................................................10
Figure 8 Scatter Diagram...............................................................................................................11
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Executive Summary
The report is the assignment questions which is used to enhance the knowledge in numeracy,
data and IT. The report aims at gaining the following outcomes: It will help to identify and
compare between the median, mean and standard deviation which is collectively known as a
central tendency. It also helps to achieve the compound interest and analysis data with the help
of graphical representation. Graphical representation helps to represent data in a simple format.
A data table is given shown in Table 1 which gives the monthly expenditure of student which
include food, Clothing, Entertainment and Charitable Giving. The scenario given is based on the
campus where the student belongs and their marital status. Based on this given data report solves
mainly four questions Question one calculates total, mean, median and standard deviation and
analysis the statistics given in the data. Question 2 gives the graphical summaries or overview of
each item described. Question third gives the relationship between four items and the marital
status with the help of Scatter diagram. Question four focuses on finding the probability that
student spend more than 500 pounds are both married and based in London. The report finds the
solution of these questions which is shown in the following report.
2

Student monthly expenditure in pounds sterling is given below in the table.
Table 1: Given data table
Name Campus Marital
Status
Food Clothing Entertainment Charitable
Giving
Jenny London S 160 230 80 0
Annie Manchester S 180 220 50 10
Haddy Manchester M 255 145 45 15
Martin Birmingham S 240 165 100 0
Ahmed London M 375 195 140 10
Sean London S 185 135 130 20
Alice London M 260 260 70 20
Belinda London M 320 140 105 15
Benjie Birmingham S 245 230 60 40
Barbara Manchester M 305 150 100 0
Liam Birmingham M 400 80 100 20
S here specifies Single.
M specifies Married.
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a) Total, Mean, Median and Standard Deviation
Mean is also known as arithmetic mean or an average of the number. It is the single value which
is used to represent the whole data. It is the degree of occurrence of central tendency. Mean helps
to conclude that the particular value is most outreached in the situation. It is generally denoted by
the A.
Formula for mean = Sum of all observation / total number of observations.
i.e. A= x1 + x2 + x3 +……………x n/ n, where n is total number of observations.
Median is if describes in simple language it is the middle numbers of the whole series. It is
generally used to the theory of probability and statistics. Median is mostly used in the robust
statistics. To calculate the mean first arrange Mingo and Speicher (2017) the series in ascending
order and if series have a total number of observations is odd, then it is evaluated as middle
number. But if even number of entries are present then it is calculated as the sum of the middle
pair divided by 2.
Standard deviation
It is used to identify the deviation or variations are present in the given set of values or data. It is
denoted by the Greek letter sigma “σ”. Population, random variable, probability distribution all
give the standard deviation as √ variance.
To calculate the standard deviation the following steps are used:
 First, find out the mean of the data.
 For every number in the table subtract the calculated mean of the above result and then
square the result.
 After finding the square of result calculate mean of that squared difference
 And last, square root the result of the above steps to get the standard deviation.
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Figure 1 Total, mean, median, standard deviation
Hence total expenditure can be calculated by adding the money spent on each of the items i.e.
food, clothing, entertainment and giving charity.
Total expenditure of Jenny = 160 + 230 + 80 + 0 = 470
Annie =180 + 220 + 50 + 10 = 460,
Haddy = 255 + 145 + 45 + 15 = 460,
Martin = 240 + 165 + 100 + 0 = 505,
Ahmed = 375 + 195 + 140 + 10 = 720,
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Sean = 185 + 135 + 130 + 20 = 470,
Alice = 260 + 260 + 70 + 20 = 610,
Belinda = 320 + 140 + 105 + 15 = 580,
Benjie = 245 + 230 + 60 + 40 = 575,
Barbara = 305 + 150 + 100 + 0 = 555,
Liam = 400 +80 + 100 + 20 = 600.
Mean of total expenditure can be calculated as = Sum of individual expenditures / total number
of entries
= 470 + 460 + 460 + 505 + 720 + 470 + 610 + 580 + 575 + 555 + 600
= 6005
Mean = 6005 / 11
= 545.9090
To calculate mean in excel the direct formula which can be used is [ = SUM (H2:H12)]
Arranging the data into increasing order = 460, 460, 470, 470, 505, 555, 575, 580, 600, 610, 720.
The middle number of the series is 555 and hence it is the median of the total expenditure
The formula which was used in the excel sheet to calculate median [ = MEDIAN (H2: H12)]
which will give the answer directly
Standard deviation can be calculated in the excel sheet by using the formula [ = STDEV (H2:
H12)].
Figure 1 shows all the above-mentioned central tendency.
Hence from the above data, we can interpret that student are based from different campus and
hence their expenditure also varies according to it. For example, students who belong to the
London campus spends more money on food. The total average amount spent by a student either
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married or single is 545.909. The need for a different item differs according to their marital
spent. There are students who do not give money to charity but spent on another item.
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b) Graphical summary
Figure 3 shows the expenditure on food by the student in the form of bars which helps to
analysis data more precisely.
Figure 2 Food
Figure 4 shows the expenditure of student in the clothing sector.
Figure 3 Clothing
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Figure 5 shows the expenditure of student in the entertainment area.
Figure 4 Entertainment
Figure 6 shows that the amount of money students give to charity.
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Figure 5 Charitable Giving
Figure 7 shows the total expenditure done by each student in each of the following sector that is
food, clothing, entertainment, charitable giving.
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Figure 6 Summarization
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