You are responsible for ensuring you understand the policy and regulations about academic misconduct. You must:
Also note that proven academic misconduct is usually required to be reported to relevant professional bodies and in some cases prospective employers which may prevent even a successful student from being admitted into their desired profession.
If you are unsure about how to complete your assessment, you should seek advice from your Module tutor and/or Module Leader.
For support and/or clarification regarding referencing and using sources in your work, ask your tutors for guidance and/or the Library team.
Online Activity -students are expected to complete and pass (40%) relevant online activity/quiz. The results page will need to be saved (screenshot) and inserted under a relevant area of the portfolio.
Section 4 is worth 61% of the final mark and consists of 13 questions.
|
Task 1 |
Task 2 |
Task 3 |
Total |
||
|
Part 1 |
Section 1 |
Pass/Fail (Skills Audit) 3% |
Pass/Fail (In class activity) 5% |
Pass/Fail (Online Activity) 5% |
39 % |
|
Section 2 |
Pass/Fail (Skills Audit) 3% |
Pass/Fail (In class activity) 5% |
Pass/Fail (Online Activity) 5% |
||
|
Section 3 |
Pass/Fail (Skills Audit) 3% |
Pass/Fail (In class activity) 5% |
Pass/Fail (Online Activity) 5% |
||
|
Part 2 |
Section 4 |
61% (13 questions) |
N/A |
N/A |
61% |
SECTION 1
This section will focus on order of operations (BODMAS); operations on positive and negative numbers; fractions and ratios.
Task 1: Skills Audit
Please note that there is no right or wrong answer. Your answers should show good reflection and awareness of your strengths and areas for improvement.
|
I know how to…. |
I can do well |
I need practice |
I’m not sure |
I can’t do |
|
1. I know what BODMAS stands for. |
Yes |
? |
? |
? |
|
2. I can apply BODMAS to a variety of calculations. |
Yes |
? |
? |
? |
|
3. I can define a fraction, numerator and denominator. |
Yes |
? |
? |
? |
|
4. I can define proper fraction, improper fraction and a mixed number. |
Yes |
? |
? |
? |
|
5. I can convert a mixed number to an improper fraction. |
Yes |
? |
? |
? |
|
6. I can convert improper fraction to a mixed number. |
Yes |
? |
? |
? |
|
7. I can add, subtract, multiply and divide fractions. |
Yes |
? |
? |
? |
|
8. I can explain the meaning of a ratio. |
Yes |
? |
? |
? |
|
9. I can work with simple ratios. |
Yes |
? |
? |
? |
Task 2: In class Activity
QUESTION 1
Reflection
Write a short reflection (approximately 100-150 words) about your personal learning experience of the topics covered in this section.
You can use the Skills Audit above to facilitate your answer. You may also consider the following points:
It is necessary for educators to understand which procedures are used by the students. Different students use different process to solve the problem (Ung et al. 2017).
QUESTION 2
Give one example of a ‘real-life’ problem or situation that involves one (or more) of the following topics:
Also, please find a solution to the problem you described.
Mr. Lewis purchased mangoes for his son and daughter. He purchased 21 mangoes. It was seen that 6 mangoes were defected. Then, he decided to distribute the rest mangoes between his son and daughter. He distributed the mangoes between his son and daughter in the ratio 1:2. How many mangoes each of them got?
Solution:
The son got (21-6)/3 =5 mangoes and the daughter got (21-6)*2/3=10 mangoes.
BODMAS rule is used to solve some problems. Using this method problems can be solved easily (Holland, Mast and Haworth 2017)
Task 3: Online Activity
Evidence (screenshot) of completing and passing relevant online quiz/activity.
Instruction:
SECTION 2
This section will focus on decimals, percentages and index numbers.
Task 1: Skills Audit
Tick the appropriate column for each skill in the list below.
Please note that there is no right or wrong answer. Your answers should show good reflection and awareness of your strengths and areas for improvement.
|
I know how to…. |
I can do well |
I need practice |
I’m not sure |
I can’t do |
|
10. I can describe the relationship between fractions, decimals and percentages. |
Yes |
? |
? |
? |
|
11. I can identify the decimal equivalent of a percent. |
Yes |
? |
? |
? |
|
12. I can identify the fractional equivalent of a percent. |
Yes |
? |
? |
? |
|
13. I can determine which concepts and procedures are needed to complete each practice exercise. |
Yes |
? |
? |
? |
|
14. I can compute answers by applying appropriate formulas and procedures. |
Yes |
? |
? |
? |
|
15. I can construct a simple index. |
Yes |
? |
? |
? |
|
16. I can interpret indexes to identify trends in a data set. |
Yes |
? |
? |
? |
Task 2: In class Activity
QUESTION 1
Reflection
Write a short reflection (approximately 100-150 words) about your personal learning experience of the topics covered in this section.
You can use the Skills Audit above to facilitate your answer. You may also consider the following points:
QUESTION 2
Give one example of a ‘real-life’ problem or situation that involves one (or more) of the following topics:
Also, please find a solution to the problem you described.
It is necessary to provide a real-life example of the above mentioned topic. It was assume that the sales of a company were £150.0 billion in the year 2011 and it was £265.75 billion in the year 2017. Therefore, it was important to calculate the relative index.
Solution: The sales were £150.0 billion in the year 2011. Therefore, the base year for the problem was 2011. The sales of the company were £265.75 billion in the year 2017. Hence, the relative index is defined as (265.75-150.0)*100/150.0 = 77.17
These decimal can be converted to fraction. It will be (7717/100)
It is very important to understand the concept of decimal and fraction numbers. It is very difficult to understand the concept (Wheeler and Champion 2016).
Task 3: Online Activity
Evidence (screenshot) of completing and passing relevant online quiz/activity
Instruction:
SECTION 3
This section will focus on introduction to statistics (mean, median, mode and range) and graphical representation of data.
Task 1: Skills Audit
Tick the appropriate column for each skill in the list below.
Please note that there is no right or wrong answer. Your answers should show good reflection and awareness of your strengths and areas for improvement.
|
I know how to…. |
I can do well |
I need practice |
I’m not sure |
I can’t do |
|
17. I know how to calculate a mean. |
Yes |
? |
? |
? |
|
18. I know how to calculate a median. |
Yes |
? |
? |
? |
|
19. I know how to calculate a mode. |
Yes |
? |
? |
? |
|
20. I know how to calculate range. |
Yes |
? |
? |
? |
|
21. I understand the statistical implications of mean, median, mode and range. |
Yes |
? |
? |
? |
|
22. I can define a line graph, bar chart and a pie chart. |
Yes |
? |
? |
? |
|
23. I can interpret and analyse graphs presented to determine what information is given. |
Yes |
? |
? |
? |
|
24. I can construct a simple line graph and bar chart. |
Yes |
? |
? |
? |
Task 2: In class Activity
QUESTION 1
Reflection
Write a short reflection (approximately 100-150 words) about your personal learning experience of the topics covered in this section.
You can use the Skills Audit above to facilitate your answer. You may also consider the following points:
QUESTION 2
Give one example of a ‘real-life’ problem or situation that involves one (or more) of the following topics:
Also, please find a solution to the problem you described.
The average temperatures of London are provided for different months. This data can be shown graphically.
|
Month |
Temperature |
|
January |
5.9 |
|
February |
6 |
|
March |
8 |
|
April |
9.9 |
|
May |
13.3 |
|
June |
16.2 |
|
July |
18.6 |
|
August |
18.6 |
|
September |
15.9 |
|
October |
12.4 |
|
November |
8.7 |
|
December |
6.9 |
Solution: Mean of the temperature= (5.9+6+8+9.9+13.3+16.2+18.6+18.6+15.9+12.4+8.7+6.9)/12 = 11.7
The data should be arranged in increasing order. Hence, the arranged data will be 5.9, 6, 6.9, 8, 8.7, 9.9, 12.4, 13.3, 15.9, 16.2, 18.6, and 18.6. Total number of observations = 12.
Hence, the mean of (12/2) = 6th and (12/2) +1 =7th observation is defined as median.
Therefore, the median = (9.9+12.4)/2 = 11.15
Frequency of 18.6 is 2 and frequency of other observations are 1.
Hence, mode = 18.6.
Minimum value of the data set is 5.9 and maximum value of the observation is 18.6. Hence range of the data is = (18.6-5.9) = 12.7.
Figure: Average temperature for different months in London
Source: Created by author
Descriptive statistics are used to get the basic idea about the data. The data can be graphically represented (Mendenhall and Sincich 2016).
Task 3: Online Activity
Evidence (screenshot) of completing and passing relevant online quiz/activity.
Instruction:
SECTION 4
QUESTION 1 [4 marks]
A mobile phone outlet has a selection of different brands for sale. of the mobiles are Samsung, 0.4 are iPhone, and the rest are HTC.
Answer (type your answer and calculations here):(a) 4/15 of the total mobiles are the mobile of HTC brand.
Calculation: 1/3 of the mobiles are Samsung. 0.4 of total mobiles are i-phones. 0.4=4/10=2/5. It is assumed that total proportion is 1. Hence, the mobiles of HTC brand = 1-(1/3 + 2/5) [It is to be noted that the L.C.F of 5 and 3 is (5*3) =15]
Calculation: There are 180 mobile phones. 1/3 of the mobiles are Samsung, 0.4 =2/5 of the phones is i-phones and 4/15 of the total phones are HTC.
Hence, the number of Samsung phones = (1/3)*180 = (180/3) = 60.
The number of i-phones = (2/5)*180 = (2*180)/5 = 320/5 = 72.
Therefore, number of HTC mobiles = 180-(60+72) = 180 – 132 =48.
QUESTION 2 [3 marks]
E-commerce sales by businesses in the UK non-financial sector were £511 billion in 2016, up from £503 billion in 2015.
Calculate the percentage change in E-commerce sales between 2015 and 2016.
Answer (type your answer and calculations here): Approximately 1.59045% E-commerce sales had been increased from the year 2015 to 2016.
Calculation: E-commerce sales in the non-financial sector of UK were £503 billion in 2015. It was £511 billion in the year 2016. Therefore, (£511-£503) = £8 billion sales had been increased from 2015 to 2016.
Hence, change in E-commerce sales between 2015 to 2016 was (8/503)* 100 = 0.015945*100 = 1.59045%
QUESTION 3 [3 marks]
E-commerce sales in 2017 were made up of £236 billion website sales which is an increase of 98.76 % from the previous year.
Calculate the E-commerce sales for the year 2016?
Answer (type your answer and calculations here): The E-commerce sales for the year 2016 were £118.7362 billion.
Calculation: It was assumed that the E-commerce sales in 2016 were £ x billion. E-commerce sales in 2017 were made up of £236 billion website sales. Therefore, the increase in sales was (£ 236- £x) billion. It was mentioned that 98.76% sales had been increased from the 2016 to 2017.
Therefore, according to the problem, [(236- x)*100/ x] = 98.76
Or, (236- x)*100 = 98.76x
Or, 23600-100x = 98.76x
Or, (100x+98.76x) = 23600
Or, 198x = 23600
Or, x = (23600/198) = 118.7362
Hence, the E-commerce sales for the 2016 were £ 118.7362 billion.
QUESTION.4 [7 marks]
In 2012, a total of £467 billion worth of website sales were generated by UK businesses. The data gathered was then used to construct the pie chart:
Using the pie chart, please answer the following questions:
Answer (type your answer and calculations here):a) Information and communication contributed the third highest (16%) in website sale.
(b) Manufacturing industry contributed the least (6%) in 2012.
(c) Retail represents 14% in the website sales.
(d) £ 28.02 billion was generated by manufacturing in 2012.
(e) £37.36 billion was more generated by retail than manufacturing.
Calculation: Website sales by industry sector in the year 2012 had been shown through a pie chart. Whole sales had contributed 31%. Website sale by information and communication sector was 16%. Other industry had contributed 23%. 6% was generated through manufacturing. Transport sector had contributed 10%.
Hence, the retail had contributed = [100-(31+23+16+10+6)] % = (100-84) % =16%
(c) Website sale presented by retail was = 100- (31+23+16+10+6) = 14%.
(d) The sales generated by manufacturing in the 2012 was = (467*6)/100 = £28.02 billion worth of website sale.
(e) The sale generated by manufacturing was = £28.02 billion worth of website sale. On the other hand the sale generated by retail was = (467*14)/100 = £ 65.38 billion.
Hence, the difference between them = (£65.38 – £28.02) = £37.36 billion.
QUESTION 5 [5 marks]
Low pay by qualification
The chart above shows the proportions of workers who are low paid by qualification level comparing 2011 with 2016. Using the chart, write a statement outlining at least three changes,that have taken place.
Answer (type your answer and calculations here): The number of low paid workers by qualification had increased in 2016 with respect to 2011.
Calculation: From the above diagram, it was seen that below 10% workers had been paid less according to their qualification i.e degree or equivalent in the year 2011. This percentage became above 10% in the year 2016. The percentage of low paid workers in the year 2011 who had completed higher education was just above the 20% while this percentage was near about 30% for the year 2016. Less than 30% workers who had completed GCE A level were paid low in 2011. This percentage increased in the year 2016. In 2011, it was seen that about 30% workers were paid less who had GCSE grades A* – C or equivalent. The above-mentioned proportion had increased in the year 2016. It became more than 40% in 2016. The percentage of other qualification holder workers who were paid less according to their qualification was 40% in the year 2011 and 50 % in the 2016. It was mentioned that below 50% of workers were paid less in 2011 that had no qualification or their qualification were unknown. It was 70% in the year 2016.
The total numbers of low-paid highly qualified workers were less in the year 2011 with respect to 2016.
The number of less paid workers with a degree of GCE A level and the number of less paid workers with a degree of GCSE grade A* to C was almost same in 2011. Similarly, these numbers were almost same in 2016. It was to be noted that the number of workers with the mentioned degree was more in 2016 than in 2011.
QUESTION.6 [6 marks]
The chart below lists the E-commerce sales of businesses in the UK non-financial sector from 2009 to 2016. Calculate the index to show the relative positions over the eight years.
The base year is2008, sales for 2008 were 334.6, (334.6 = 100).
|
2009 |
2010 |
2011 |
2012 |
2013 |
2014 |
2015 |
2016 |
|
|
£ billio |
375.1 |
418.9 |
494.1 |
473.6 |
544.7 |
513.5 |
502.8 |
510.5 |
|
Index |
12.104 |
25.194 |
47.669 |
41.542 |
62.791 |
53.467 |
50.269 |
52.570 |
Answer (type your answer and calculations here and in the chart above): Calculation: The base year is 2008. Sales for 2008 were 334.6. Sales for 2009 were 375.1. Therefore, relative index for 2009 with respect to 2008 is (375.1-334.6)*100/334.6 =12.104.
Sales for 2010 were 418.9. Thus, the relative index for 2010 with respect to 2008 is (418.9-334.6)*100/ 334.6 = 25.194.
Sales for 2011 were 494.1 and sales for the base year were 334.6. Hence, the relative index for the year 2011 with respect to 2008 is (494.1 -334.6)*100/334.6 =47.669.
Sales for 2012 were 473.6 and sales for 2008 were reported as 334.6. Hence, the required relative index is (473.6-334.6)*100/334.6 = 41.542
Sales for 2013 were 544.7 and sales for the base year were 334.6. Therefore, the required relative index is (544.7-334.6)*100/334.6 = 62.791.
It was reported that the sales were 513.5 in 2014. Therefore, the relative index is (513.5-334.6)*100/334.6 = 53.547
The relative index for the year 2015 with respect to 2008 is (502.8-334.6)*100/334.6 = 50.269 as the sales for 2015 were 502.8 and it were 334.6 for the year 2008.
Sales for the year 2008 were 334.6 and the sales for the year 2016 were 510.5. Hence, the required relative index is (510.5-334.6)*100/334.6=52.570.
Please answer questions 8 – 12 using data provided below:
QUESTION 8 [2 marks]
What percentage of people living in London, live in Wandsworth?
Answer (type your answer and calculations here): Approximately, 3.76% people living in London, live in Wandsworth.
Calculation: Total number of people in London is 8173900 and the total number of people in Wandsworth is 307000. Therefore, the required percentage = (307000/8173900)*100 = 3.76.
QUESTION 9 [2 marks]
In Havering, how many people are aged 65 and over?
Answer (type your answer and calculations here):Approximately, 42222 people are aged 65 and over in Havering.
Calculation: Total number of people in Havering is 237200.About 17.8% people of them are aged 65 and over in Havering. Hence, the required number of people is = (237200*17.8)/100 =42221.6. The number of people cannot be in fraction. Therefore, there are 42222 people of age more than or equal to 65.
QUESTION 10 [3 marks]
How many more people are aged between 20 and 64 in the City of London than Kingston upon Thames?
Answer (type your answer and calculations here):There are 5162488 more people in city of London than Kingston upon Thames of age between 20 and 64.
Calculation: There are 160100 people in Kingston upon Thames. About 63.4% people are between 20 to 64 years. Hence, total number of people in Kingston upon Thames of age between 20 years to 64 years is = (106100*63.4)/100 = 101503.4. The number of people must be integer. Hence, total people of Kingston upon Thames of age between 20 years to 64 years are 101503. Similarly, the number of people aged 20 years to 64 years can be calculated in the city of London. Total population in the city of London is = 8173900. Approximately, 64.4% of total population are aged between 20 and 64 years in the city of London. Therefore, total number of people in London in this particular age group is = (8173900*64.4)/100 = 5263992. Hence, (5263992-101503) =5162488 more people are aged between 20 and 64 in the city of London than Kingston upon Thames.
QUESTION 11 [4 marks]
If one third of the people live in the City of London, one fifth of the population live in Inner London and the rest in Outer London.
What is the ratio of City of London to Outer London?
Answer (type your answer and calculations here):The ratio of city of London to Outer London is 21:2.
Calculation: Total population in England and Wales is 56075900. It is assumed that one third of the population live in city of London. Then, the number of population in the city of London is (56075900/3) =18691967.It is also assumed that one fifth of the population live in inner London. Hence, the number of population in inner London is = (56075900/5) = 11215180. Hence, the population in outer London is = (18691967 – 11215180) = 7476787.
Hence, the proportion of City of London to Outer London = (18691967/7476787) = 21/2. Therefore, the required ratio is 21:2.
QUESTION 12 [6 marks]
Taking into account individual aged 5-19, in Barnet, Islington, Tower Hamlets, City of London, Hackney, Sutton, and Greenwich, please calculate the following:
Answer (type your answer and calculations here):(a) Mean=239298.5, (b) Median=43197, (c) Range = 1384612.
Calculation: Total population of age 5-19 in Barnet is = (356400*18)/100 = 64152. Total population of age 5-19 in Islington is = (206100*14.3)/100 =29472. There are
(254100*17)/100 = 43197 people of age group 5 to 19 years in Tower Hamlets. The number of people in this specified group in the City of London is = (8173900*17.3)/100 = 1414085. The number of people in this specified group in Hackney is = (246300*17.3)/100 = 42610. The number of people of age group 5 to 19 years in Sutton is = (190100*18)/100 = 34218. There are (254600*18.6)/100 = 47356 people of age group 5 to 19 years in Greenwich.
(a) Hence, the required mean is = (64152+29472+43197+1414085+42610+34218+47356)/7 = 239298.5
(b) The values are arranged in ascending order. Then, the values are 29472, 34218, 42610,43197,47356,64152 and 1414085. Seven cities of England and Wales are taken into consideration. Therefore, median is the (7+1)/2 = 4th value of the arrangement. Hence, the required median is 43197.
(c) In Islington, population of this specified group is less among the all mentioned cities. It is 29472. In the City of London, the population of this particular group is more than all specified cities. It is 1414085. Therefore, the required range is = (1414085 – 29472) =1384612.
QUESTION 7 [6 marks]
Household work status and the income distribution
Data source: Households Below Average Income, DWP. 2016
Using the data presented in the bar chart above, answer the following questions:
Answer: Approximately 14% of all of the adults in the lowest percentile are in work full time.
Answer: About 20% of people in the richest 20% has at least one adult that is in work.
Answer: About 10% of people in the middle have pensioner households.
QUESTION.13. [10 marks]
Think about your modules and amount of time you spend studying per week, create a table and answer following questions
|
Module/Weeks |
Week1 |
Week 2 |
Week3 |
Week4 |
Week5 |
Week6 |
Week7 |
Week8 |
|
Numeracy1 |
7 |
6.5 |
6 |
5 |
4.6 |
4.3 |
4.2 |
4 |
|
EAP1 |
5 |
4.8 |
4.5 |
4.3 |
4.2 |
4.1 |
3.5 |
3 |
|
EBWO3001 |
4 |
3.8 |
3.6 |
3.3 |
3.1 |
2.9 |
2.7 |
2.5 |
|
ICSK3005 |
2 |
1.8 |
1.4 |
1.2 |
1 |
0.5 |
0.4 |
0.2 |
|
18 |
16.9 |
15.5 |
13.8 |
12.9 |
11.8 |
10.8 |
9.7 |
Answer (type your answer and calculations here): (a) Bar charts are plotted based on the entries.
Source: Created by Author
(b) It is seen from figures that more times are spent in first week. Comparatively, less time is provided in 2nd to 8th week. Least time is taken in 8th week. It is also seen that more time is provided in Numeracy 1. Less time is taken in EAP 1 module. Less time is taken in EBWO3001 module than the above-mentioned two modules. Least time is provided to ICSK3005 module.
(c) Total time spent for Numeracy1 module is 41.6 hours. Total 33.4 hours are spent in EAP1. It is also to be noted that about 25.9 hours are spent in EBWO3001. It is noted that 8.5 hours are provided for ICSK3005 module.
|
Modules/Week |
week1 |
week2 |
week3 |
week 4 |
week 5 |
week6 |
week7 |
week 8 |
Total |
|
Numeracy 1 |
7 |
6.5 |
6 |
5 |
4.6 |
4.3 |
4.2 |
4 |
41.6 |
|
EAP1 |
5 |
4.8 |
4.5 |
4.3 |
4.2 |
4.1 |
3.5 |
3 |
33.4 |
|
EBWO3001 |
4 |
3.8 |
3.6 |
3.3 |
3.1 |
2.9 |
2.7 |
2.5 |
25.9 |
|
ICSK3005 |
2 |
1.8 |
1.4 |
1.2 |
1 |
0.5 |
0.4 |
0.2 |
8.5 |
|
Total |
18 |
16.9 |
15.5 |
13.8 |
12.9 |
11.8 |
10.8 |
9.7 |
109.4 |
References:
Holland, C.K., Mast, T.D., Haworth, K.J. and Abruzzo, T.A., 2017. Biomedical research at the image-guided ultrasound therapeutics laboratories. The Journal of the Acoustical Society of America, 141(5), pp.3681-3681.
Mendenhall, W.M. and Sincich, T.L., 2016. Statistics for Engineering and the Sciences. Chapman and Hall/CRC.
Ung, T.S., Kiong, P.L.N., Manaf, B.B., Hamdan, A.B. and Khium, C.C., 2017, April. Cognitive analysis as a way to understand students’ problem-solving process in BODMAS rule. In AIP Conference Proceedings (Vol. 1830, No. 1, p. 050002). AIP Publishing.
Wheeler, A. and Champion, J., 2016. Stretching Probability Explorations with Geoboards. Mathematics Teaching in the Middle School, 21(6), pp.332-337.
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