MBF3C&Culminating&Activity&Day&3& && Name& · PDF fileMBF3C – FOUNDATIONS OF COLLEGE MATHEMATICS MR. G. PEARSON 29. Thefollowinggraphappearedinalocalnewspaper: + + a) Whattypeofdistributiondoesthisgraphrepresent?[1+

MBF3C – FOUNDATIONS OF COLLEGE MATHEMATICS MR. G. PEARSON

MBF3C Culminating Activity Day 3 Name _________________________

STATISTICS PART A – Definitions [34 MARKS]

Define each of the following terms from this unit.

1. population

2. sample

3. simple random sample

4. stratified random sample

5. voluntary response sample

6. cluster sample

7. convenience sample

8. systematic sample


9. primary source

10. secondary source

11. mean

12. median

13. mode

14. quartiles

15. categorical data

16. continuous data

17. discrete data


PART B – Multiple Choice [11 MARKS]

Identify the choice that best completes the statement or answers the question in the box provided.

1. Categorical data can be best represented by:

A – Bar Graph B – Histogram

C – Pie / Circle Chart D – A and C only

2. The Principal wants to host a Meet-‐The-‐Teacher Barbeque, but wants to know if it

should be combined with Parent-‐Teacher Interviews or be held as a separate event. Which survey method would provide a non-‐biased sample?

A – Ask the teachers by putting questionnaires in their mailboxes. B – Send a questionnaire for parents home with students. C – Create an online survey and ask parents and teachers to complete the survey. D – Ask the Vice-‐Principal for her opinion.

3. The marks on a Unit Test were as follows:

65, 45, 87, 67, 74, 78, 92, 52, 90, 66, 74, 76, 81, 88

This data would be best represented by:

A – bar graph B – circle / pie graph

C – histogram D – any of the above

4. A data set consists of 11 values. They are listed in order from least to greatest. What

is the median for the data set?

A – the 5th value B – the 6th value

C – the average of the 5th and 6th values D – the average of the 6th and 7th values

5. What conclusion can you not make from this pie/circle chart?

Favourite Music of Students At SCI

A – Most students at SCI listen to Country music.

B – About half of the students of SCI listen to Country music.

C – The actual number of students at SCI who listen to Country Music.

D – About the same number of students listen to Metal, Pop, and Hip-‐Hop combined as listen to Country.

E – Nickelback Sucks.

Country

Metal

Pop

Hip Hop

Other


6. James has taken five tests. His scores are 65%, 74%, 91%, 74%, and 76%. James has the choice of taking any measure of central tendency as his overall grade.

Which of these measures of central tendency should he take?

A – mean B – median

C – mode D – does not matter

7. If a goalie wanted to calculate his GAA (Goals Against Average), which of the

following measures of central tendency would they use?

A – mean B – median

C – mode D – does not matter

8. A bias can occur in:

A – a survey

B – a sample C – interpretation of data D – all of the above

9. A local politician wants to establish an effective platform for the upcoming election,

but only has a few days to determine what issues the voters are most concerned about. What would be the most effective way to find out?

A – Conduct a telephone survey ensuring that he contacts a selection of residents

from all parts of his community. B – Set up a booth downtown and ask passers-‐by. C – Put a survey up on the internet. D – Walk into all of the local businesses on the main street and survey everyone

inside. 10. Kira conducts a survey of student’s marks and analyses the data. She calculates that

for her results, there is a very low standard deviation. This means:

A – the data is scattered and difficult to draw conclusions from. B – most students had a low mark. C – most of the student’s marks were very close to the mean of the whole group. D – her data was inaccurate and she needs to repeat her survey.

11. Rob wanted to analyse the amount of time each player on his soccer team spends

on the field during a game. When he graphed his results on a histogram, he found that there were trends at 45 minutes and 10 minutes. This is an example of:

A – normal distribution. B – bimodal distribution. C – trimodal distribution. D – using the wrong type of graph to display data.


PART C – Short Answer [28 MARKS]

Write your answer in the space provided.

27. A jack-‐in-‐the-‐box manufacturer has been getting some complaints because of faulty products, and decides to implement some product testing. Currently, the manufacturer has four assembly lines, and each run is identified with a batch number. Kelly has been hired to design product control, and she has a few options available to her. Identify the type of sample in each of the following survey methods.

a) Kelly instructs the floor supervisor to select 50 jack-‐in-‐the-‐boxes from a single

assembly line each day for testing. [1 MARK]

b) Kelly instructs the floor supervisor to install counters on each assembly line, and have a machine pick every 1500th jack-‐in-‐the-‐box that passes for testing. [1 MARK]

c) Kelly instructs the floor supervisor to select 5 jack-‐in-‐the-‐boxes each hour from any assembly line for testing. [1 MARK]

d) Kelly instructs the floor supervisor to randomly select 1% of number of jack-‐in-‐the-‐boxes from each batch produced each day for testing. [1 MARK]

28. A survey question is worded as follows: “The amount of money that the Ontario government

spends on EQAO each year would be enough to employ 1300 Educational Assistants. Do you think that the province should scrap the EQAO testing?” Describe the bias that could influence the results of this survey, and rewrite the question so that it is without bias. [3 MARKS]


29. The following graph appeared in a local newspaper:

a) What type of distribution does this graph represent? [1 MARK] b) Which age group had the most accidents? [1 MARK]

c) How could you improve the graph to make better comparisons between the numbers of accidents for different age groups? [1 MARK]

d) Complete the following table, and graph your new results. [5 MARKS] 16-‐25 26-‐35 36-‐45 46-‐55 56-‐65 66-‐75 76+

e) What new conclusions can be made from this new graph? [1 MARK]

0

5

10

15

20

25

16-‐25 26-‐32 33-‐38 39-‐42 43-‐45 46-‐48 49-‐55 56-‐65 66-‐75 76+

Num

ber o

f Acciden

ts in Hun

dred

s

Age Range

Accidents In Muskoka


30. The results are finally in! The marks from the Geometry Unit Test are as follows (%):

96 84 92 79 89 93 98 82 87 84 56 96 34 64 77 79 96 84 83 85 80 97 84 72 72 85 92 75 98 94 97 88 97 90

a) Find the mean, median, mode, first quartile, third quartile, and range for the marks.

[6 MARKS]

MEAN MEDIAN MODE 1ST QUARTILE 3RD QUARTILE RANGE b) Create a tally and frequency chart for the above data. [2 MARKS]

<50% 50%-‐59% 60%-‐69% 70%-‐79% 80%-‐89% 90%-‐100%

Tally

Frequency c) Graph the results below. [4 MARKS]


PART D – Thinking / Inquiry [17 MARKS]

Write your answers in the space provided. 31. Design a stratified-‐sampling procedure to survey the students in Simcoe County District

School Board to determine if students feel that there would be a benefit to introducing middle schools. Middle schools would be designed for Grades 7 and 8 only. Be specific in your design. [4 MARKS]

32. When is a voluntary sample the best choice to collect data? Provide a detailed example.

[3 MARKS] 33. A friend of yours is trying to determine how to budget for college/university. Since you are

a statistics expert, your friend comes to you for advice. Describe who you would survey, how you would survey, and identify the type of survey. Be specific. [4 MARKS]


34. For a science project, a student tested how many kilometres can be traveled on a motorcycle with a single tank of fuel. The results were as follows: 266, 250, 295, 281, 304, 298, 275, 271

a) Determine the range for this data set. [1 MARK]

b) Calculate the variance and standard deviation for this data. [5 MARKS]

𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒 = (𝑥! −𝑚𝑒𝑎𝑛)! + (𝑥! −𝑚𝑒𝑎𝑛)! + (𝑥! −𝑚𝑒𝑎𝑛)! +⋯+ (𝑥! −𝑚𝑒𝑎𝑛)!

𝑛

𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 = 𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒 Variance Standard

Deviation 𝑥! −𝑚𝑒𝑎𝑛 (𝑥! −𝑚𝑒𝑎𝑛)! (𝑥! −𝑚𝑒𝑎𝑛)! (𝑥! −𝑚𝑒𝑎𝑛)!

𝑛 (𝑥! −𝑚𝑒𝑎𝑛)!

𝑛

90

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MBF3C&Culminating&Activity&Day&3& && Name& · PDF fileMBF3C – FOUNDATIONS OF COLLEGE MATHEMATICS MR. G. PEARSON 29. Thefollowinggraphappearedinalocalnewspaper: + + a) Whattypeofdistributiondoesthisgraphrepresent?[1+