Faculty of Computing, Engineering and Science Assessment Cover Sheet and Feedback Form 2018-19…

Faculty of Computing, Engineering and Science
Assessment Cover Sheet and Feedback Form 2018-19
Module Code:
AM0S05
Module Title:
Application of Mathematical
Skills
Module Team:
Filippo Cavallari, Angelica Pachon
Assessment Title and Tasks:
Portfolio Sheet 3
Assessment No.
3
Date Set:
dd-mmm-yyyy.
Submission Date:
dd-mmm-yyyy.
Return Date:
dd-mmm-yyyy.
IT IS YOUR RESPONSIBILITY TO KEEP RECORDS OF ALL WORK SUBMITTED
Marking and Assessment
This assignment will be marked out of 100%
This assignment contributes to 20% of the total module marks.
Learning Outcomes to be assessed (as specified in the validated module
descriptor https://icis.southwales.ac.uk/ ):
1) Apply a range of basic calculus and statistical techniques, and interpret the solutions
appropriately.
2) To understand the basic calculus and statistics behind relevant applications and to be
able to identify and perform relevant mathematical and statistical techniques
appropriately.
Provisional mark only: subject to change and / or confirmation by the Assessment
Board
AM0S05 PORTFOLIO QUESTIONS
AM0S05 PORTFOLIO QUESTION SHEET 3
• This portfolio sheet is worth 20% of your module and is marked out of 40.
• You should attempt all questions, giving answers correct to 2 decimal places where
appropriate.
• Fill in the Answers Template document and submit this
together with a document with the results in excel
using your STUDENT ID NUMBER as the file name for your submission.
Please submit only one document!
If you fail to do this it may not be possible to attribute your work to you and so you
may get a zero for this coursework.
• Submission is via Turnitin ONLY by midday on Friday 22/03/19.
• In some questions you will see the term α:
{ If the last two digits of your STUDENT ID NUMBER are greater than or equal
to 10, and less than 85, then let the last two digits of
your STUDENT ID NUMBER be α.
{ If the last two digits of your STUDENT ID NUMBER is less than 10 then
add 10 to the last two digits of your STUDENTID NUMBER and let this
number be α.
{ If the last two digits of your STUDENT ID NUMBER is 85 or more then
subtract 10 from the last two digits of your STUDENT ID NUMBER and let this
number be α.
• If you have any questions about how to submit the coursework, how to use the
Answers Template, or how to find your α value, then it is your responsibility
to ask your lecturer during your tutorial class.
• NOTE: if you use the wrong α value you will get zero for any question which uses α.
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AM0S05 PORTFOLIO QUESTIONS
Exercises
1. (13) The height (measured in cm) of a sample of 65 students was recorded as follows.
174 179 172 189 180 172 181 183 182 176 189 181 174
162 186 178 178 185 184 182 184 183 179 164 182 178
177 168 175 181 188 185 181 178 168 175 175 178 186
183 177 176 183 182 173 173 N 183 177 184 181 174
180 170 188 192 175 171 182 177 195 178 183 178 173
where N = α + 155 if 10 ≤ α ≤ 35, N = α + 130 if 36 ≤ α ≤ 60, and N = 190 if α > 60.
Find
a (i) 1st quartile, (ii) 3rd quartile, (iii) mean, (iv) sample standard deviation and (v)
population standard deviation. Use “Insert Function” in excel.
b Construct a grouped frequency table for this data using five classes (160-167, 168-175,
176-183, 184-191, 192-199) and draw a bar chart.
c Draw an histogram and compare with the bar chart.
2. (35) A retailer has four shops in a city. Daily sales (in thousand pounds) from the last 10
days have been collected in the following table.
Shop 1 Shop 2 Shop 3 Shop 4
12 18 19 13
8 19 3 20
10 2 25 10
12 18 20 13
14 11 22 12
α α α α
11 3 25 11
7 17 20 9
13 4 22 10
11 17 26 8
a Use the “Insert Function” to calculate: (i) Max, (ii) Min, (iii) Mean, (iv) Median, (v)
First Quartile, (vi) Third Quartile and (vii) Interquartile Range for each Shop and for
the whole set of data.
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AM0S05 PORTFOLIO QUESTIONS
b Construct a table with the total sales (of the last 10 days) for each shop. Use this table
to draw a pie chart.
3. (10) The table below gives the numbers of wrong answers in a sample of exams:

No. of fails:

0 1 2 3 4 5 6 7 8 9 10

No. of exams:

4 5 10 24 α 27 23 14 16 7 3

Use the frequency table to calculate:
a (i) mean, (ii) median, (iii) mode and (iv) sample variance for the number of wrong
answers per exam, without using “Insert Function”. For the sample variance show all
the necessary steps as we did in class (show me all the columns you created).
b Use the frequency table and draw a bar chart.
4. (9) We have to study the relationship between the monthly e-commerce sales (y) and the
online advertising costs (x). The next table shows the survey results for 10 online stores for
the last year.

Store

1 2 3 4 5 6 7 8 9 10

y

368 340 605 954 331 556 376 337 α + 350 630

x

1.7 1.5 2.8 5 1.3 2.2 1.3 1.4 1.9 3.0

a Calculate the value of the Pearson correlation coefficient between x and y using excel.
b Find the equation of the line of regression of y on x using excel
c Draw the scatter diagram, including the line of regression.
5. (8) Differentiate the following equations to find dy=dx
(a) y = 2×2 + α tan x
(b) y = x-2(α + x) – 2 sin x + 4 cos x
(c) y = (x – 2)(αx + 2) + 5ex – 2 sin x
(d) y = x2-5x+α
x3 + ln x22
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END OF QUESTIONS
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