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GET READY FOR STATISTICS

READING ASSIGNMENT:Read about Census, Poll, Study Pages 268 272Investment 1 Question 2 b, d, g Page 273

Handout (MEQ exam) Questions 1, 2Read about Representative Sample Pages 275 278Investment 2 Question 1 c, d, e Page 279Handout (MEQ exam) Questions 3, 4Read About Sources of Bias Pages 282 287Pop Quiz 21 Question 3 Page 296Handout (MEQ exam) Question 5Read about Summary Page 290

MEQ exam questions:

1. Which of the following describes a census?

A) Oliver interviews the 1274 students in his school to find out what their favourite food is.B) Oliver interviews a doctor to learn about the effects of a high cholesterol level.C) Oliver interviews some of his friends and relatives to find out about the eating habits ofQuebecers.D) Oliver interviews 30 students in his school to find out how much milk teenagers drink.

2. Which of the following describes a census?

A) Alan visits a number of retailers in his area to determine the cost of a swimming pool.B) A property assessor visits every home in a town to determine the number of residents whoown a swimming pool.C) A swimming pool dealer consults some chemists to find out how disinfectant pellets affect thepH of water.D) A manufacturer consults some consumers so he can build the type of swimming pool theywant.

3. The following table shows the distribution of the student population in a givenschool. A sample of 180 students is required. This sample must be representative ofthe population distribution shown in the table.

Number of Girls Number of BoysFirst Cycle 360 345Second Cycle 240 255

How many girls from the second cycle should be in the sample? Show all your work.

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4. The following table shows the distribution of the 15 000 voters in a given town.

Area Women MenDowntown 1200 1100South End 1500 1500

East End 1000 1200North End 2800 1200West End 1700 1800

A sample of 750 people is required. This sample must be representative of thepopulation distribution shown in the above table. How many men from the west end oftown should be in this sample? Show all your work.

5. The following article appeared in a local newspaper.

Poll says students spend enough time in school

This was the main finding of a poll of 200 Qubec residents. The poll results areshown in the table below.To cut costs, the polling firm interviewed 200 people aged 20 to 25, most ofwhom come from the island of Montral.

Do students spend enough time at school?Women Men

Yes 60% 80%No 20% 10%

Undecided 20% 10%

Identify and explain two sources of bias in this poll.

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CORRECTION SHEET FOR READING ASSIGNMENT

Investment 1, Question 2b: census d: poll g: study (survey)

MEQ 1: A

MEQ 2: B

Investment 2, Question 1c: no (he only interviewed people who attend, not those who werent coming)d: no (only people in two cities were polled; the population of Montreal is more thantwice as large as that of Quebec City)e: yes (selected randomly, not just from those whom he knew were satisfied; over 7years will help to see long-term satisfaction)

MEQ 3: 36 girls from the second cycle.Total population = 1200;

240

1200 180=

x

MEQ 4: 90 men from the west end of town1800

15000 750=

x

Pop Quiz 21, question 3a: her friends are likely to be from the same school; 25 students may not be enough torepresent 18 class groups of about 30 students each or about 540 students; she is likely

to have phoned only students who actually have income.b: she could have polled an equal number of students from each school; the studentschosen randomly (perhaps alphabetically).

MEQ 5: people aged 20 to 25 are not in school themselves, and they are not oldenough to have children in school; most people polled lived in the largest city

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DAY ONE:Refer to the answer sheet given with this set of handouts.

Discuss the vocabulary census, poll, study (survey) and discuss the questionsstudents were assigned on these concepts.

Note that the first two MEQ questions on examples of census can also be discussed asto what the other three choices are examples of.

MEQ 1: A is a census; B is a study (survey); C is a poll, but biased; D is a poll, againprobably biased.

MEQ 2: A is a poll; B is a census; C is study (survey); D is a poll.

Discuss representative sample, and discuss the questions assigned to this concept.

Discuss sources of bias, and discuss the questions assigned to this concept.

If you have time, discuss other questions from the textbook pages.

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DAY TWO: Together with the class, work through an example where you areconstructing a stem and leaf table and a box and whisker plot. A good example is foundon page 297 in the student textbook. Discuss quartiles, quarters and interquartilerange.

The textbook does not show how to construct a stem and leaf table, and the studentshave not studied this before, so the data (bowling scores) from page 297 is given in itsraw form here so that together you can construct the table together.

123 99 139 100 88 86 133 100 153 112 93 107 73

131 169 95 105 111 91 138 77 80 102 116 128

After constructing the stem and leaf, answer questions on page 297.

Answers: a: 169 and 73 b: 105 c: 92 d: 129.5

e: 6 6 6 6 f: yes divide data into 4 equal parts

Then construct the box and whiskers plot (not shown in textbook) to display theanswers to the questions.

(I have not used an exact scale here youll need to do so at the board)

If you want to do this on the graphing calculator as well, you will need to enter the datapoints, and do a stats plot (see pages 298 and 300 for a review of the method).

The range of the data is calculated as 169 73 = 96.The interquartile range is calculated from Q3 Q1 = 129.5 92 = 37.5.

Homework: Page 304 Question 7 b, d.Page 305 Question 9 a, c, d.

7392 105 129.5

169

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DAY THREE: Take up the homework first.

Question 7: b: min is 85, Q1 is 99.5, median is 109, Q3 is 121, max is 164.

d) From the plot it could be that approximately half of the drivers exceeded the limit by

10 km, but the plot does not show the number of drivers who were caught at 109 km.From the plot we cannot tell how the data is dispersed in each quarter, we only see thelimits of each quarter.

Question 9: a: minimum is 21, maximum is 35, Q1 is 28, Q2 (median) is 30, Q3 is 32,range is 35 21 = 14, interquartile range is 32 28 = 4.c: Yes. There are 200 pupils, and half of them weigh 30 kg or more.d: Answers can vary here. Possibilities include: half of the students weigh between 28and 32 kg. There is a greater spread of weights in the first quarter than in any otherquarter, etc.

COMPARING DIFFERENT SETS OF DATA

Examine and discuss the example on page 302 of two different sets of data from twodifferent baseball teams.Please note that they have incorrectly used the term quartile in questions f and ginstead of quarter.

Homework: Page 345 Question 7MEQ exam question 1,2 (given on next page)

Answers to homework:

Question 7: a) True b) cant tell c) True d) True e) cant tell f) True

MEQ question 1: B (you might want to discuss answer D)

MEQ question 2:93 is the maximum mark, and is not represented in the data list.Q3 is 73, and it is not represented in the data list.Since 69.5 is the median, and 70 is represented, the missing mark on the other side ofthe median is 69.The first quartile is missing one data point (7 marks must be less than 61) so the lastmissing mark will be in that range.

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MEQ questions:

1. The following box-and-whisker plot represents the annual salary of employees in alarge company.

Which of the following statements is definitely TRUE?

A) The mean salary is $30 000.B) Half the employees earn between $24 000 and $42 000.C) The salaries are more densely concentrated between the second and third quartiles.D) There are more employees who earn over $42 000 than employees who earn under

$24 000.

2. The marks on a history test for a class of 30 students are represented by thefollowing box-and-whisker plot.

The following are the marks for 26 of the 30 students:

43 54 55 56 58 60 61 65 66 66 66 67 6870 71 71 71 71 71 71 74 77 77 79 86 88

Find the four missing marks. Explain why you chose each mark.

3. The data below shows the height, in cm, of 300 children.

58, , 83, 84, 84 85, 86, , 200

90 children 210 children

What percentile rank should be assigned to a child whose height is 85 cm?

4. The trainer at a fitness club recorded the number of consecutive sit-ups that eachmember can do. The results are given below:

50, 50, 51, , 59 60, 61, 61, , 69 71, 72, 73, , 78 80, 80, 80, , 95

83 members 91 members 80 members 47 members

Fred did 72 sit-ups in a row. What is Freds percentile rank?

12 000 24 000 30 000 42 000 72 000

937369.56143

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DAY FOUR: Quintile and Percentile Rank. Use the example on page 319 to show therelationship between quartiles, quintiles and percentiles on large sets of data.Look at the report card on page 308 to stimulate a practical discussion on the format ofreport cards. Note that when using quartiles the lowest quarter is the first quarter, butwhen using quintiles, the highest quintile is the first quintile!

Work together on question 2 on page 310, and question 3 from 1998 MEQ exam, onprevious page.

Solutions:Question 2: a) there are 25 students, so those in quintile 1 are 178, 179, 180, 185, 190b) 145 is in quintile 3. c) quintile 3

MEQ question 3: 30 or 31

Homework:Page 310 Question 4MEQ question 4 (previous page)

Answers to homeworkQuestion 4: There are 21 different marks in the first set of results (counting for examplethe 3 marks of 24 as one mark). Put 4 marks in the first 2 and last 2 quintiles, and 5 inthe centre one. In the second set of results, there are also 21 different marks, so dividethe data as above.On the first exam, Isabelles mark was lower than on her second exam, but the range ofmarks for the entire class was lower, as were the maximum and minimum values. Onthe first exam, Isabelles mark is in the second quintile, but on the second exam, hermark is in the third quintile, so in comparison to the rest of the class, she did better onthe first exam.

MEQ 4: 58 or 59

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DAY FIVE: SUMMARYReview the concept of quintile and percentile, using page 317 question 11.

a) Her history rank is quite low, and her mathematics rank is low as well.b) 71 is the 59th percentile, so 59% of 25000 = 14750 students

c) In both physics and geography she received a mark of 71 percent, but in geographyshe is in a lower percentile.

Discuss together page 332 question 1 a, b, c (with the addition of asking for range andinterquartile range for the data).

a) (75), 76, 77 b) 2 or 3 depending on how you separate the quintilesc) median = 63, Q1 = 58, Q3 = 69, min = 50, max = 77range: 77 50 = 27 interquartile range: 69 58 = 11

Discuss together page 332 question 2 a, b and c with the modification in c of

give the position of the person who obtained

a) Maki has a percentile of 81, her brother 84b) her brotherc) the 3601st participant.

Homework: Page 333, question 4. Note question d should say quarter not quartileMEQ question (as follows)

Sophies students obtained the following marks on a provincial examination last year.

45 56 57 58 60 60 62 63 67 6868 68 69 70 71 72 73 73 73 7373 73 75 76 79 79 81 88 90 95

The following box-and-whisker plot is based on province-wide results for the sameexamination.

Compare the results in Sophies class with the province-wide results. Your comparisonmust consist of 4 conclusions.

Homework solutions:Question 4: a) B b) A c) 25/50 = _ d) the second quarter e) B

MEQ: Students should make a box-and-whisker plot and can compare range,interquartile range, median, etc.

9 59 70 77 100