statistic

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Statistics

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Nayef_22

FC301-PRACTICEtest-Midmoduleexam.docx

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FC301- PRACTICE mid-module Exam

There are 20 questions

Answer ALL questions

The total number of marks is: 60 marks

The time allowed for the exam is 90 minutes

1. This is an open book exam; therefore, you need to provide Formula sheet.

2. The use of a calculator is allowed

3. At the start of the examination, you need to be able to see/download the question book in pdf format or Microsoft word format:

4. Write your Student ID (Pxxxxxx) and your name at the top of each page.

5. Read each question carefully, taking note particularly on how to give your numerical answers. Some questions ask for an exact number, whilst others ask for it to be rounded to 2s or 3sf or 1 dp or 2dp.

6. In multiple choice questions, please select one answer only: a, b, c or d

7. Read the task information carefully before you begin to write.

8. Use clean and A4 paper to Write your answer.

9. Write in black or blue ink. Use pencil for drawing graph only.

10. Your answer must be readable and clear.

11. Label each question and part.

12. Cross out any mistakes.

13. The submission link will be open for last half an hour of this exam.

14. The submission link will close exactly 45 minutes after duration of the exam.

15. You must submit your answer in pdf format only.

Good Luck!

FC301 Statistics Practice mid module exam

Q1) Speed, temperature and height are all examples of which type of data [Equation]<m:oMath xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><m:d><m:dPr><m:ctrlPr><w:rPr xmlns:w="http://schemas.openxmlformats.org/wordprocessingml/2006/main"><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math" w:cs="Arial" /><w:b /><w:i /><w:lang w:eastAsia="x-none" /></w:rPr></m:ctrlPr></m:dPr><m:e><m:r><m:rPr><m:sty m:val="bi" /></m:rPr><w:rPr xmlns:w="http://schemas.openxmlformats.org/wordprocessingml/2006/main"><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math" w:cs="Arial" /><w:lang w:eastAsia="x-none" /></w:rPr><m:t>-2,1</m:t></m:r></m:e></m:d></m:oMath>[Equation]<m:oMath xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><m:r><w:rPr xmlns:w="http://schemas.openxmlformats.org/wordprocessingml/2006/main"><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math" w:cs="Arial" /><w:lang w:eastAsia="x-none" /></w:rPr><m:t xml:space="preserve"> </m:t></m:r><m:d><m:dPr><m:ctrlPr><w:rPr xmlns:w="http://schemas.openxmlformats.org/wordprocessingml/2006/main"><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math" w:cs="Arial" /><w:b /><w:i /><w:lang w:eastAsia="x-none" /></w:rPr></m:ctrlPr></m:dPr><m:e><m:r><m:rPr><m:sty m:val="bi" /></m:rPr><w:rPr xmlns:w="http://schemas.openxmlformats.org/wordprocessingml/2006/main"><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math" w:cs="Arial" /><w:lang w:eastAsia="x-none" /></w:rPr><m:t>4,4</m:t></m:r></m:e></m:d></m:oMath> ? (1 mark)

a. Quantitative discrete

b. Qualitative nominal

c. Quantitative continuous

d. Qualitative ordinal

Q2) Which type of data can be defined as ‘numerical, measurable and whole or limited numbers’ [Equation]<m:oMath xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><m:r><m:rPr><m:sty m:val="bi" /></m:rPr><w:rPr xmlns:w="http://schemas.openxmlformats.org/wordprocessingml/2006/main"><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math" w:cs="Arial" /><w:lang w:eastAsia="x-none" /></w:rPr><m:t xml:space="preserve">m = </m:t></m:r><m:f><m:fPr><m:ctrlPr><w:rPr xmlns:w="http://schemas.openxmlformats.org/wordprocessingml/2006/main"><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math" w:cs="Arial" /><w:b /><w:i /><w:lang w:eastAsia="x-none" /></w:rPr></m:ctrlPr></m:fPr><m:num><m:r><m:rPr><m:sty m:val="bi" /></m:rPr><w:rPr xmlns:w="http://schemas.openxmlformats.org/wordprocessingml/2006/main"><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math" w:cs="Arial" /><w:lang w:eastAsia="x-none" /></w:rPr><m:t>3</m:t></m:r></m:num><m:den><m:r><m:rPr><m:sty m:val="bi" /></m:rPr><w:rPr xmlns:w="http://schemas.openxmlformats.org/wordprocessingml/2006/main"><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math" w:cs="Arial" /><w:lang w:eastAsia="x-none" /></w:rPr><m:t>2</m:t></m:r></m:den></m:f></m:oMath> [Equation]<m:oMath xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><m:d><m:dPr><m:ctrlPr><w:rPr xmlns:w="http://schemas.openxmlformats.org/wordprocessingml/2006/main"><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math" w:cs="Arial" /><w:b /><w:i /><w:lang w:eastAsia="x-none" /></w:rPr></m:ctrlPr></m:dPr><m:e><m:r><m:rPr><m:sty m:val="bi" /></m:rPr><w:rPr xmlns:w="http://schemas.openxmlformats.org/wordprocessingml/2006/main"><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math" w:cs="Arial" /><w:lang w:eastAsia="x-none" /></w:rPr><m:t>6,8</m:t></m:r></m:e></m:d></m:oMath> (1 mark)

a. Quantitative discrete

b. Qualitative nominal

c. Quantitative continuous

d. Qualitative ordinal

Q3) Which type of data is represented graphically on a Histogram? (1 mark)

a. Quantitative discrete

b. Qualitative nominal

c. Quantitative continuous

d. Qualitative ordinal

Q4) What is the measure which shows the value at which 25% of a data set score equal to or higher? (1 mark)

a. Mean

b. Lower quartile

c. Upper quartile

d. Median

Q5) Which measure of average is most affected by the presence of an outlier? (select one answer) (1 mark)

a. Mode

b. Mean

c. Median

d. Middle

[Equation]<m:oMath xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><m:r><m:rPr><m:sty m:val="bi" /></m:rPr><w:rPr xmlns:w="http://schemas.openxmlformats.org/wordprocessingml/2006/main"><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math" w:cs="Arial" /><w:lang w:eastAsia="x-none" /></w:rPr><m:t>4</m:t></m:r></m:oMath>

Q6. Nine students took a quick test (with 20 questions). Their marks were recorded;

16 9 9 12 20 19 15 11 14

Calculate:

Q6a) The mean mark (to 2sf) (1 mark)

Q6b) The median mark (2 marks)

Q6c) The mode (1 mark)

Q6d) The range of the marks (1 mark)

Q6e) The Standard deviation of the marks (Use Mean to 2sf and n-1 and give final answer to 1sf) (3 marks)

Q7.

Q7a) According to the Box plot above, approximately how many percent of students scored between 400 and 560 on their SAT Maths scores? (2 marks)

Q7b) According to the Boxplot above, what is the range of SAT Math scores? (1 mark)

Q7c) According to the Boxplot above, what is the Lower quartile value of SAT Math scores? (1 mark)

Q8.

The ages (in years) of 15 employers in a small company are recorded in this table;

34	43	42	54	25
21	42	36	42	60
38	28	47	39	51

Q8a) Calculate the median. (2 marks)

Q8b) Calculate the lower quartile value (1 mark)

Q8c) Calculate the upper quartile value (1 mark)

Q8d) Calculate the Interquartile range (1 mark)

Q9.

Q9a) What is the modal group? (1 mark)

a. 70-99

b. 0-9

c. 30-39

d. 40-49

Q9b) Using the Cumulative frequency graph, what would be the estimate for the Median age? (1 mark)

a. 45 years

b. 44.5 years

c. 36 years

d. 52 years

Q9c) Using the Cumulative frequency graph, what would be the estimate for the Interquartile range? (1 mark)

a. 32

b. 15

c. 25

d. 28

Q10.

Image result for grouped frequency table

Using Class mid-points, calculate an estimate of the Mean weight (to 2sf) (3 marks)

Q11.

Image result for histogram frequency density

The Histogram above shows the distribution of ribbons of varying lengths between 0 and 60cm

Q11a) How many ribbons are in the 35 < l ≤ 45 group? (1 mark)

a. 10

b. 2

c. 18

d. 20

Q11b) Which group has a frequency of 8? (1 mark)

a. 0 < l ≤ 20

b. 20 < l ≤ 30

c. 30 < l ≤ 35

d. 35 < l ≤ 45

Q12.

This pie chart shows the mobile phone brands used by a sample of 300 people

Q12a) What percentage of the sample own an iphone ? (1 mark)

Q12b) What percentage of the sample own an ‘other’ brand of mobile phone? (1 mark)

Q12c) How many more people own Samsung mobile phones compared to Motorola? (1 mark)

Q13.

Q13a) If there were 240,000 tonnes of Glass in total in the year 1990, how many tonnes of it was recycled in that year? (1 mark)

Q13b) Which material saw the biggest increase between the years 2000 and 2010? (1 mark)

a. Paper/Paperboard

b. Metals

c. Glass

d. Plastics

Q13c) Which of the following statements is true? (1 mark)

a. Glass is the material which is recycled most

b. Since 1990 there has been a consistent increase in the recycling of Plastics

c. Since 1960 the recycling of Paper/Paperboard has always increased

d. The recycling of Metals has decreased since 1990

Q14.

14a) Which is the most likely coefficient of correlation value (r value) to represent the correlation shown in the above scatter diagram? (1 mark)

a. 0.99

b. -0.72

c. 1

d. 0.79

14b) Using the best fit line in the above scatter diagram, what would be the predicted amount of carbon monoxide if the Traffic volume is 350? (1 mark)

a. 4

b. 15

c. 20

d. 8

Q15.

The correlation of a pair of variables (Miles per gallon and Weight) can be seen in the scatter diagram below.

Image result for negative correlation scatter plot with r value

15a) Describe the correlation shown in the scatter diagram (1 mark)

a. Positive and strong

b. Perfect and negative

c. Negative and weak

d. Negative and strong

15b) Calculate the Coefficient of Determination (to 2dp) (2 marks)

15c) What would the Coefficient of Determination show? (1 mark)

a. Miles per gallon is approximately 87% responsible for the change in weight

b. Miles per gallon is approximately 76% responsible for the change in weight

c. Miles per gallon is approximately 75% responsible for the change in weight

d. Miles per gallon is approximately 24% responsible for the change in weight

Q16.

1997	1998	1999
Q1	Q2	Q3	Q4	Q1	Q2	Q3	Q4	Q1	Q2	Q3	Q4
16	10	9	14	18	12	11	17	22	16	13	20

The 4 point moving averages are as following:

x, 12.75, 13.25, 13.75, 14.5, 15.5, 16.5, 17, y

16a) Calculate the first 4 point moving average x (exact value) (2 marks)

16b) Calculate the final 4 point moving average y (exact value) (2 marks)

16c) Which of the following statements describes what is shown by the Time series graph above? (1 mark)

a. There is an increasing trend and Q4 always sees the highest Sales

b. There is an increasing trend and Q1 always sees the highest Sales

c. There is a decreasing trend and there is no seasonal variation

d. There is an increasing trend and Q2 always sees the lowest Sales

Q17.

Year	1990	1994	1998	2002	2006	2010	2014	2018
Temperature	16.2	16.3	15.3	15.9	17.5	15.4	16	17.6
Chain base Index numbers	100.6	93.9	103.9	110.1	88.0	103.9	x

17a) Using the information in the above table, calculate the Simple Index number, comparing temperature from 2018 and 1990 and using 1990 as the base year (to 3 sf) (2 marks)

17b) Complete the chain base Index number calculations. What is the value of x ? (2 marks)

17c) Calculate the 2019 Temperature if the Index number for years 2018 and 2019 (using 2018 as base year) is 101.70455 (use exact value and give answer to 1dp) (2 marks)

Q18.

A shirt costs £25.00 but in a sale its price is decreased by 10%

18a) How much does the shirt cost (in £), after the decrease in price? (2 marks)

18b) At the end of the sale, everything is ‘70% off original price’

How much does the shirt cost (in £) now? (2 marks)

Q19.

A university Physics module is assessed by a mid-term exam, a lab report, and an end of term exam.

The weighting of marks awarded for the module is as follows:

Mid-term exam: 30%

Lab report: 20%

End of term exam: 50%

Q20.

What is the final (overall weighted average) mark of a student who got these marks?

Mid-term exam: 75/100 marks

Lab report: 70/100 marks

End of term exam: 87/100 marks (3 marks)

End of exam

Cumulative frequency graph to show the distribution of Age

0 10 20 30 40 50 70 100 0 4 10 25 54 76 87 89

Age (years)

Cumulative frequency

iphone Samsung Huawei Motorola Nokia Other 90 69 54 45 27 15

Multiple Bar chart to show Recycling Rates over time

Paper/Paperboard 1960 1970 1980 1990 2000 2010 17 16 21 27 42 62 Glass 1960 1970 1980 1990 2000 2010 2 1 5 20 21 27 Metals 1960 1970 1980 1990 2000 2010 1 3 8 24 35 35 Plastics 1960 1970 1980 1990 2000 2010 2 6 8

Year

Percent Recycled

Scatter diagram to show the relationship between Traffic volume and Carbon Monoxide level in the atmosphere

50 55 80 110 100 150 175 200 230 240 250 248 251 260 290 320 340 400 425 2 3 5 3 9 10 11 13 7 11 11 13 12 12 15 10 16 15 18

Traffic Volume (# of cars observed per day)

Carbon Monoxide level

Time series graph to show Ice cream sales over 3 years

Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 1997 1998 1999 16 10 9 14 18 12 11 17 22 16 13 20

Year

Ice cream sales (millions $)