Essay: Practice Problems And Solutions For Statistics And Numeracy.

E-commerce Sales in 2017

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:

• Reflect on your learning
• How did you contribute in the class?
• What went well?
• Are there any areas for improvement?

2.Give one example of a ‘real-life’ problem or situation that involves one (or more) of the following topics:

• Order of operations
• Operations on positive and negative numbers
• Fractions
• Ratios

Also, please find a solution to the problem you described.

3.Evidence (screenshot) of completing and passing relevant online quiz/activity.

 Instruction:

1. Complete your online quiz/activity, (GSM Learn).
2. Take a screenshot.
3. Copy and paste the screenshot here.

4.Give one example of a ‘real-life’ problem or situation that involves one (or more) of the following topics:

• Introduction to statistics (mean, median, mode and range)
• Graphical representation of data

 Also, please find a solution to the problem you described.

 The total fertility rates of some cities of England and Wales are provided as follow.

Cities	TFR
City of London	1.76
Islington	1.41
Tower Hamlets	1.58
Barnet	1.88
Baxley	2.09
Kingston upon Thames	1.74

5.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.

a)What fraction of the mobiles is HTC?

b)If there are 180 mobiles altogether, how many of each brand is in the outlet?

6.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?

7.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:

a) Which industry contributed the third highest in website sales?

b) Which industry contributed the least in 2012?

c) What percentage does Retail represent in website sales?

d) What much was generated by manufacturing in 2012?

e) How much more was generated by retail than manufacturing?

8.Low pay by qualification

                                                 

Website Sales by UK Businesses

 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.

9.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 is 2008, sales for 2008 were 334.6, (334.6 = 100).

	2009	2010	2011	2012	2013	2014	2015	2016
£ billion	375.1	418.9	494.1	473.6	544.7	513.5	502.8	510.5
Index	112.104	125.194	147.669	141.542	162.791	153.467	150.269	152.57

Please answer questions 10-14 using data provided below:

                                                                   

10. What percentage of people living in London, live in Wandsworth?

11. In Havering, how many people are aged 65 and over?

12. How many more people are aged between 20 and 64 in the City of London than Kingston upon Thames?

13. 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?

14. Taking into account individual aged 5-19, in Barnet, Islington, Tower Hamlets, City of London, Hackney, Sutton, and Greenwich, please calculate the following:

1. Mean
2. Median
3. Range

15. Household work status and the income distribution

                                                             

Using the data presented in the bar chart above, answer the following questions:

       a) What percentage of all of the adults in the lowest percentile, are in work full time?

       b) What percentage of people in the richest 20% has at least one adult that is in work?

       c)  What percentage of people in the middle have pensioner households?

16. 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	2	2	2	2	3	3	3	4
EAP1	2	1	2	1	2	2	3	3
EBWO3001	1	1	2	2	3	2	3	3
ICSK3005	1	1	3	2	2	3	3	4
	6	5	9	7	10	10	12	14

a) Create a bar chart based on your entries above.

b) What does your data tell you, comment on the pattern (if any)?

c) What is the average time you spend studying throughout 8 weeks for all of your modules? Show your calculations.

d) Create a table to show individually the total number of hours spent studying for each one of the four modules over the 8 weeks .

E-commerce Sales in 2017

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.

                                                                      

Website Sales by UK Businesses

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.

Total Fertility Rates

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-

100. i) The value of indexes for all the years after 2008 are greater than 100.
101. ii) The value of index is minimum (112.104) in the year 2009.

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.

Population Statistics

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