Data Management and Statistical Analysis Assignment - Semester 1

This document presents a comprehensive solution to a data management assignment, covering various aspects of data analysis and statistics. The solution begins by identifying and explaining the differences between primary and secondary data sources, followed by a discussion on appropriate chart...Read More

Managing Data
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Contents
QUESTION 1..................................................................................................................................1
(a) 3 main sources to collect primary data and secondary data...................................................1
(b).................................................................................................................................................1
(c) Best type of chart to represent the variable Tesco Stock Price..............................................2
(d).................................................................................................................................................3
QUESTION 2..................................................................................................................................3
(a) Probability for Mike to spend over £10 on journeys to campus............................................3
(b) Frequency for students living over 1 mile away from the campus........................................3
(c) Modal group...........................................................................................................................3
(d) Using simple interest..............................................................................................................4
(e) Using compound interest........................................................................................................4
QUESTION 3..................................................................................................................................5
(a).................................................................................................................................................5
(b) The 95% confidence interval for the test scores....................................................................5
(c).................................................................................................................................................5
QUESTION 4..................................................................................................................................5
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QUESTION 1
(a) 3 main sources to collect primary data and secondary data
Primary data sources
 Surveys
 Experiment
 Observation
Secondary data sources
 Books
 Journals
 Blogs
(b)
Arithmetic mean of the stock price
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The mean or average of the Tesco stock price is 229.50, the workings of calculating this
Mean value is attached above in form of an Excel print screen with formula of calculating mean.
The median of the stock price
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The median value of Tesco stock price is 228.5, this value is gained by using Median
formula in Excel and print screen of those workings is attached above.
The monthly percentage change on 01/04/2020
Formula = (Current month stock price – Previous month stock price / Previous month stock
price) * 100
= (218.8 – 228.8 / 228.8) * 100
= (10 / 228.8) * 100
= -4.37%
The monthly percentage change on 01/04/2020 is -4.37% indicating a reduction of stock
prices in this month.
(c) Best type of chart to represent the variable Tesco Stock Price
Best chart for representing Tesco Stock Prices is line chart as it can effective present
growth values and stock prices are subject to growth.
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(d)
Primary data is a firsthand data which is collected from sources like surveys and interviews.
Such primary data can be both qualitative and quantitative, so the statement of Abbi stating that
primary data is qualitative data is not correct. To understand this concept, Abbi should consider
that the primary data which is collected through sources like surveys is quantitative data and the
primary data collected through sources like interviews is quantitative data.
QUESTION 2
(a) Probability for Mike to spend over £10 on journeys to campus
P(event) = Number of event / Total events
P(over £10) = 1 / 19
(b) Frequency for students living over 1 mile away from the campus
Frequency of students living over 1 mile away = 10 + 20 + 19 = 49
(c) Modal group
A modal group is the group with highest frequencies. For the category of Amount Spent, £,
the modal group is 5.00 – 9.99 as this group has highest frequencies of 77 students. The
workings and formulas of such analysis is attached below:
Distance to Campus (miles)
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Amount spent, £
0.1
to
0.25
0.26
to
1.0
Over
1.0
Total
frequencies
0 – 4.99 35 26 10 71
5.00 – 9.99 18 39 20 77
10.00+ 4 14 19 37
(d) Using simple interest
Principle = £200 per month
= £200 * 12 * 3 = 7200
A = P (1 + rt)
A = £7200 (1 + 3% * 3 years)
= £7200 (1.09)
= £7848
(e) Using compound interest
Principle = £7200
Formula of compound interest
A = P (1 + r / n) ^ nt
A = £7200 (1 + 0.03 / 12) ^ (12 * 3)
= £7200 (1.0025) ^ (36)
= 7200 (1.0025^36)
= 7200 * 1.094
= £7877
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QUESTION 3
(a)
31 marks
(b) The 95% confidence interval for the test scores
As no sample size is provided in the question, the sample size of applicants is assumed to be 100.
Formula of calculating confidence interval = ±z √ [p (1 - p) / n]
Z value of the 95% confidence interval is 1.96
N is 100
Mean (x) = 70
Standard deviation = 10
= ± 1.96 (10 / 10)
= 1.96
Therefore, margin of error is ±1.96
Lower value = 70 – 1.96 = 68
Upper value = 70 + 14.96 = 72
So, 95% confidence interval is 68 to 72 marks
or 70 ± 1.96
(c)
 Distribution shown in graph is uniform distribution
 Probability density function is P (18 <= x <= 24)
 Probability of the blue area is P(18<= 1/15 <= 24)
P(1/15) = 1(24 – 18)
P(1/15) = 1 / 6
P(1/15) = 0.16
QUESTION 4
(a) Statistical relationship along with characteristics
The scatter plot provided for sales and advertising expenditure is representing a trend line
having uphill pattern. This uphill pattern shows positive relationship between sales and
advertisement expenses. The characteristics of such relationship are:
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 If advertisement expenses of Little Liu Ltd increases, then the sales of this organisation
also increases. In scatter plot, it can be seen that advertisement expense is going left to
right, the sales is showing an uphill pattern of growth.
 The second characteristic of this relationship is that these two variables has linear
relationship as the scatter plot is showing a straight line.
 The third characteristic is considered to be the strength of relationship. The correlation
coefficient is calculated of such variables which is determined to be 0.85 which implies
sales and advertisement expenses share a strong relationship. The workings of
calculating correlation coefficient are given as Excel print screen below:
(b) Values of parameters of the relationship
The equation of linear relationship is y = mx +c
The calculation of values of parameter is shown below:
Year Advert.
Expenditure (X) Sales (Y) X*Y X^2
(x, £000) (y, £000)
2008 8 30 240 64
2009 12 40 480 144
2010 11 29 319 121
2011 5 29 145 25
2012 14 43 602 196
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2013 3 17 51 9
2014 6 20 120 36
2015 8 30 240 64
2016 4 22 88 16
2017 9 40 360 81
Total 80 300 2645 756
Particulars Details
m NΣxy – Σx Σy / NΣ x^2 – (Σx)^2
(10*2645)-(80*300)/(10*756)-(80)^2
(26450-24000)/(7560-6400)
2450 / 1160
2.11
Particulars Details
c Σy - m Σx / N
(300-(2.11*80))/10
13.12
The equation is: y = 2.11x + 13.12
(c) Explaining the relationship and making recommendation to Little Liu Ltd
The relationship between sales and advertisement expenses of Little Liu Ltd is positive,
strong and linear which helps to reaching at the conclusion that if Little Liu Ltd increases its
advertisement expenses, the sales of such company also increased. The chances of such
increment are also high as there is a strong correlation considering this, a recommendation is
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made that Little Liu Ltd should increase their expenses of promotion and advertisement as by
this they will be able to increase the sales revenue which will lead towards higher profits and
growth.
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