1.The learning was very compact from my end. I have enjoyed the class. I was so attentive in the class. It was very interesting. I successfully solved the assignment without help of anyone. The experience was good. It is seen that the concept of BODMAS is very necessary in daily life. More times are required to solve a problem using the BODMAS rule. I need some times to be familiar with the function of different types of brackets. I improved in the section of use of fractions and ratios significantly. I would like to apply this concept in real-life in future.
2.The addition, subtraction, multiplication and division are carried out when we buy any commodity from a shopping mall. The base price is printed on the product say a Cadbury. The offer is applied with the Cadbury of a certain percentage. We calculate the subsidy amount by multiplying printed price and rate of offer. Then, we subtract that subsidy amount from the costMendenhall, W.M. and Sincich, T.L., 2016. Statistics for Engineering and the Sciences. Chapman and Hall/CRC. price. The price of the Cadbury gets decreased. This way, we calculate the final selling price of the commodity (Jansen, Spink and Saracevic 2000). The seller can calculate his/her profit or loss by multiplying 100 by profit amount or loss and dividing total cost price. The problem of calculation of every component of buying and selling method is calculated with the help of order of mathematical operations. Without, the use of order of operations the task would be very difficult to execute.
It is assumed that total sale for 2011 in a company was £140 billion and it was £ 145.5 billion in 2016. Then, the relative index for 2016 with respect to 2011 is (145.5-140)*100/140 = 3.93. It can be converted in fraction as 393/100.
While we are interested to find the comparison of mixture quantities, speed of two cars, weights of two persons or income of two families, then representation of fraction method becomes difficult to understand (Samuels, Witmer and Schaffner 2012). Then, ratio method is very useful.
3.
4.This problem can be shown graphically as follows.
Figure: Total fertility rate for different cities
Source: Created by author.
Mean = (1.76+1.41+1.58+1.88+2.09+1.74)/6 = 1.74333
The data can be arranged as 1.41, 1.58, 1.74, 1.76, 1.88 and 2.09.
The median = (1.74+1.76)/2 = 1.75
Every observation has frequency 1. Hence, it is a multi-modal distribution.
Range= (2.09-1.41) = 0.68
5.a) The calculated decimal fraction of “Samsung” mobile phone =
The decimal fraction of iPhone = 0.4.
The total decimal fraction of both “Samsung” mobile and “iPhone” = (0.333+0.4) = 0.733
Total fraction of all the “Samsung”, “iPhone” and “HTC” mobile = 1.
Therefore, the calculated fraction of HTC mobile = (1-0.733) = 0.277.
b) The total number of mobiles all together = 180.
The number of “Samsung” mobiles
The number of “iPhone” = (180*0.4) = 72.
The number of HTC mobile = (180-(60+72)) = (180-132) = 48.
6.The amount of E-commerce sales in 2017 = £236 billion.
The E-commerce sales have increased from 2016 to 2017 by 98.76%.
Therefore, the percentage of sales in 2017 has become = (100%+98.76%) = 198.76% of 2016.
The calculated amount of E-commerce sales
7.The contribution of Retail industry = (Total% – (Wholesale%+Information & Communication% + Transport%+Manufacturing%+Other%)) = (100% – (23%+6%+10%+16%+31%)) = (100%-86%) = 14%.
a) The third highest amount of contribution is observed in the sector of “Information and communication industry” (16%) preceding “Wholesale” industry (31%) and “Other” industries (23%).
b) Manufacturing industry has provided the least amount of website sales in 2012 only by 6%.
c) In 2012, the “Retail” industry in UK has contributed 14% in website sales.
d) UK businesses has generated a total of £467 billion by UK businesses in 2012.
The “Manufacturing” industry in that year had contributed 6% amount of the website sales.
Hence, the calculated amount of profit contributed by “Manufacturing” industry = (£467*6%) billion = £28.02 billion.
e) The percentage of profit provided by “Retail” industry greater than “Manufacturing” industry = (14%-6%) = 8%.
Therefore, the amount of profit provided by “Retail” industry greater than “Manufacturing” industry = (£467 * 8%) billion = £ 37.36 billion.
9.
According to the drawn bar chart-
iii) The value of index is maximum (162.791) in the year 2013.
iv) The value of index has grown significantly from the year 2009 to 2011. The index is lowered in the year 2012 and then again increased in the year 2013. Finally, a deficit is observed in the year 2014.
10. The calculated percentage of people living in London, live in Wandsworth =
11. The total number of people living in “Havering” is 237200.
The percentage of people over the age 65 is 17.8% in “Havering”.
Hence, the number of people whose age is 65 and over in “Havering” = (237200*17.8%) = 42222.
12. The population of “City of London” = 7400.
The number of people whose ages are between 20 years and 64 years in the City of London = (7400*75.7%) = 5602 (approximately).
The population of “Kington upon Thames” = 160100.
The number of people whose ages are between 20 years and 64 years in “Kington upon Thames” = (160100*63.4%) = 101503.
The difference between the number of people whose ages are in between 20 to 64 for the “City of London” and “Kington upon Thames” = (101503-5602) = 95902.
Therefore, the number of people who are more aged in “Kington upon Thames” than “City of London” in the range 20 to 64 years is 95902.
13. As per question, the fraction of population in the “City of London” =
The fraction of population in the “Inner London” =
The fraction of population who live in “Outer London” = (1-
The ratio of population in “City of London” with respect to “Outer London” =
The ratio of population in “City of London” with respect to “Outer London” =
14.
|
Population |
Percentage of population in the age range 5-19 years |
Population of 5 to 19 years |
|
|
Barnet |
356400 |
18% |
64152 |
|
City of London |
7400 |
8.10% |
599 |
|
Greenwich |
254600 |
18.60% |
47356 |
|
Hackney |
246300 |
17.30% |
42610 |
|
Islington |
206100 |
14.30% |
29472 |
|
Sutton |
190100 |
18% |
34218 |
|
Tower Hamlets |
254100 |
17% |
43197 |
|
Mean |
37372 |
|
Median |
42610 |
|
Maximum |
64152 |
|
Minimum |
599 |
|
Range |
63553 |
The mean of the population of the considered cities off UK in the age range 5 to 19 years = 37372. The median of the population of the considered cities off UK in the age range 5 to 19 years = 42610. The range of the population of the considered cities off UK in the age range 5 to 19 = (Maximum population – Minimum population) = (64152-599) = 63553.
15. a) The lowest percentage of all the adults in the lowest percentile in work all full time is approximately 14%.
b) The percentage of people in the richest 20% has at least one adult that is in work = 20%.
c) The percentage of people in the “Middle” have pensioner households = 10%.
16. Figure: Frequency distribution of various types of study hours for modules per week
Figure: Frequency distribution of total number of study hours for various modules in all weeks
Figure: Frequency distribution of week wise total number of study hours for modules
b)The grouped bar chart of number of study hours for different modules for different weeks indicate that as the time passed, the total number of study hours increased.
For Numeracy and ICSK3005, most of the study hours are allotted in last or 8th week (4 hours). For EAP1, most of the study hours are allotted in 7th and 8th week (3 hours). For EBWO3001 module, most of the study hours are allotted in 5th, 7th and 8th week (3 hours).
Note that, total number of study hours in all eight weeks is maximum for Numeracy1 module (21 hours) followed by ICSK3005 (19 hours). The minimum total study hours is minimum for EAP1 (16 hours).
In the second bar chart, as the weeks proceed, the average study hours of all the modules increase. Maximum of the study hours (14) is observed in 8th week whereas minimum of the study hours (5) is seen in 2nd week. Week 10 afterwards, the total number of study hours in all modules is greater than 10.
c)Table: The table of average number of hours to solve the various types of modules throughout 8 weeks
|
Module/Weeks |
Average |
|
Week1 |
1.5 |
|
Week 2 |
1.25 |
|
Week3 |
2.25 |
|
Week4 |
1.75 |
|
Week5 |
2.5 |
|
Week6 |
2.5 |
|
Week7 |
3 |
|
Week8 |
3.5 |
d) Table: The table of frequency distribution showing total number of hours spend for various modules per week.
|
Module/Weeks |
Numeracy1 |
EAP1 |
EBWO3001 |
ICSK3005 |
Total |
|
Week1 |
2 |
2 |
1 |
1 |
6 |
|
Week 2 |
2 |
1 |
1 |
1 |
5 |
|
Week3 |
2 |
2 |
2 |
3 |
9 |
|
Week4 |
2 |
1 |
2 |
2 |
7 |
|
Week5 |
3 |
2 |
3 |
2 |
10 |
|
Week6 |
3 |
2 |
2 |
3 |
10 |
|
Week7 |
3 |
3 |
3 |
3 |
12 |
|
Week8 |
4 |
3 |
3 |
4 |
14 |
|
Total |
21 |
16 |
17 |
19 |
73 |
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