StatisticsEssential Math 12

Mr. Morin

Name:Slot:

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Review

Measures of Central Tendency - Mean, Median, Mode

Trimmed Mean —

Weighted Mean

Percentile Rank

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ReviewConvert the following into a percent.

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Arrange the following numbers in ascending order.

___%__%

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Arrange the fllowing numbers in descending order.

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Measures of Central Tendency - Mean, Median, and Mode

Example 1Jon bought tickets to Minnesota Timberwolves in the last year. These are theprices that he paid: $2)5, $3544, $84.04, $4497, $27, $2)5, $6526,$3S:44, $55,,23, $344. Calculate the three measures of central tendency.

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Example 2Create a set of 5 numbers that has a mean of 6, a mode of 4 and a median of 5.

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Example 3During a week Billy logged the hours he worked: 7 hours twice, 4 hours once

and 6 hours 4 times.Calculate the three measure of central tendency.

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Measures of Central Tendency - Questions

1. Find the three measures of central tendency for the following dataset.12, 1, 1, 12,

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Mode:

Median: 7- 05_3

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2. One month, Breff buys Iwo lunches at $2.95 each, five lunches at $3.75each, and one lunch at $5.25. Find the mean, median, and mode for the

amount Breft spends on lunches during the month.

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3. Ralph wrote four tests and received the following marks 50%, 73%, 80%and 54%.

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a. Calculate the mean and median

Ib. If a fiffh test is wriffen, what is the lowest score that Ralph could

receive on the test if he wants a mean mark of 70%.

4. Consider The following table

Payroll Information for Morin Manufacturing#of Union

Position employees Salary Total Salary Member

President 1 $ 250,000 7’D NoVice President’ T, 2 $ 130,000 24 NoManager 2 $ 75,000 ) T NoSupervisor $ 50,000 ) YesLabourer ‘_ : 30) $ 40,000 toO YesPayroll Clerk $ 37,000 lO YesCustodian 1 5 $ 35,000 r1oD YesSales 10 $ 32,000 YesAdminStaff \ 6 $ 24,000 Yes

Total:[ Total:

a. Determine all three measures of the central tendency for allemployees’ salaries.

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b. What data points are influential in the mean?.j soo

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c. Determine the three measures of central tendency for union CDemployees’ salary,

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d. As a parl of a bargaining commiftee for union employees, howwould you argue that the salaries are low? Explain.

0e. In this circumstance; what measure of central tendency do you

think gives the best picture of the salaries of all the company’semployees?

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***We will be discussing the previous example at for anunderstanding of weighted averages***

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5. Identify the measure of central tendency that is the most imporlant in each ofthe scenarios.

Scenario Rationale

Working in a store, placing an order forThe number of soda cans by size: 355m1,710m1, or 1L.

Measuring the weight of a hockey team,Lv

Seffling an argument with a friend todetermine who the best bowler is bycomparing scores.

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Trimmed Mean

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ExampleJamie is an Olympic skater and received the following scores: 6.0, 5.8, 5.7, 5.7,

6.0, 4.2, and 6.0.a) Calculate the mean.

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b) Identify an outlier.‘e— 4

c) If the lowest and highest scores are dropped, calculate the trimmed mean.

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d) Dropping only the outlier of the group calculate the trimmed mean.

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Trimmed Mean - Questions

1) Create a four number dataset where an influential point (outlier) brings downthe average.

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2) Create a four number dataset where an influential point (outlier) brings upthe average. I T

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3) Brian is a small business owner. The following table summarizes the hourly wage thathe pays each employee.

$12 $42 $12 $16

$12 $12 $15 $15

a) Calculate: ,R ,12. ic,Ici3 L—J

Mean:

Median: 3’l (,JA’%.

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b) Identify the outlier(s).

c) After removing the outlier, calculate the I L’ ‘

Mean: 133

Median: I .

Mode: I

How does removing the outlier affect the mean, median, or mode?

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4) The median price of gasoline in Manitoba towns are as follows:

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a) Calculate the

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Median: 2C

Mode:_lz

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b) Remove any outliers, and calculate the trimmed mean.

c) In your opinion, what is the best measure of gas prices in Manitoba? Explain.(Mean, median, Mode or trimmed mean.)

5) The scores for a unit test in mathematics are listed below.

30 I 45 I 45 55 I 65 I170J I 70 I 70 75 80 I 95

a) State the median fr i

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b) The teacher decides not to count the lowest mark. Indicate whether thefollowing measures will increase, decrease, or stay the same

Mean:_______ Mode:______ 0

Winnipeg $1 .221LChurchill $1 .99/LLorefte $1,29/LFalcon Lake $1.2?/LFun Flon $1 .5/LThePas $12/LPrawda $1.28LMiami $1 ,271/L

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Weighted Average (Weighted Mean)

Weighted Average - Questions1) Describe a situation where weighted averages are more useful than the

regular mean.

2) Calculate the Weighted Average for Billy in Canadian History

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3) In Grade 11 Essentials, a person’s term mark is worth 70% of their final grade,

while the exam is worth 30% of their final grade. Julie is a student in this class

and receives a mark of 84% for her term and 50% on her exam. What is her

overall mark?

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AverageWeightCategory Mark

Assignments 90 10%

Tests 65 60%

Final Exam 60 30% /3

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4) (As the same weights as the above question) Ryan receives a mark of 35% onhis term mark, and his goal is to receive 50% final. What does he need to get C)for an exam mark?

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5) You are a mathematics teacher at Miles Macdonell. The categories forassigning marks are

• Homework• Assignments• Quizzes• Tests• Exam

Determine the weight that you would assign to each category in you class.Write at least three sentences that explain your rationale.

Percentile RankB

Percentile Rank = —x 100n

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Examples

1. Sam scores 82% on her biology exam, There were 199 other students who

wrote the same exam. 135 students received a lower score, What is her

percentile ranking?

2. Wendy wrote a science test. She is in the 96th percentile, yet unhappy with

her mark. Provide a possible explanation.

3. Using the following information about a class of chemistry test results,

determine the percentile rank for the students who achieved 72.

18 42 52 59 68 73 83 8927 45 53 61 70 75 83 9038 45 56 64 82 85 9040 48 58 67 72 \ 83 85 97

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Percentile Rank - Questions1. Baby Isla was at Dr. MacDonald’s office for her 3-month check-up. She

weighed l4lbs and l5oz, When compared to 900 ojjr babies, Islaweighed more than 180 other babies. What is her percentile rank forweight at 3 months?

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2. A total of 3286 students wrote a university entrance exam. Poka had ascore of 891 out of 1200. There were 318 students who scored lower than891.

a. What is Poka’s percentile ranking?

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b. To apply for an entrance scholarship, Poka had to score in the top10%. Did Poka score high enough to be able to apply for thescholarship? Explain.

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3. In Lovepreet’s band class of 50 students, 26 students can play fewer

instruments than Lovepreet, and 4 students can play as many instruments

as she can.a. Find her percentile rank.

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c. What percent of students play more instruments than Lovepreet?

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4. The following statistics are available on The family income for acommunity that has a total of 2200 families:P25: $15,500 P75: $42,750P50: $28,475 P85: $64,250

What percent of the families earn $28,475 or less?

ii. How many families earn $28,475 or less?

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b. What percent of families earn $a4,250?

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II Jb. What does this percentile rank mean?

c. What percent of families earn $42,750 or less?

d. What percent of families earn more than $15,500 but less than orequal to $64,250?

e. How many families earn more than $15,500 but less than or equal to$64,250?

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5. The following is a listing of the weights of professional hockey players (Ibs)

“ 139 c - 157 189 81--145 177 199. i9O —150ri6O 182 19 1a0/ 182 , 173 18O. - 150 1 á3;

153 175 193k. 157 ‘r

a. Determine the percentile rankings for each of the followinQweights9 p (0c

— ?i. 160 lbs 2(

ii. 190 lbs

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b. What percentage of players weighs more than 177 pounds?

a. Jody and Carol play on two different basketball teams, They wereboth ranked for points scored on their teams.

• Jody ranks in the 90th percentile on her team.• Carol ranks in the 75th percentile on her team.

Explain whether it can be determined which player scored more points.

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