Math 3202 Section 2.1 Opening Investigationmrmcdonaldshomepage.weebly.com/uploads/1/3/9/2/13921997/mat… · Math 3202 Section 2.1 Opening Investigation: Math 3202 Section 2.1 Mean,

Unit 2: Working With Data Measures of Central Tendency

1. Work with a partner. Measure each other’s height to the nearest inch.

2. Collect height data from all members of the class. List the male andfemale data in a table in ascending order (from least to greatest).

Height of Males Height of Females

3. What is the middle value for males? For females? The middle value isthe median.

4. Does any data value appear more than once for males? For females?If yes, what is the data value? This value is the mode of the data set.

5. Determine the sum of the values in each data set. Divide the sum bythe number of values. This value is the mean of the data set.

Math 3202 Section 2.1 Opening Investigation

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6. Imagine you wish to describe the typical height of a grade 12 boy and agrade 12 girl. Based on the three measures of central tendency you have determined – mean, median, and mode – which do you think best describes the typical height of a grade 12 boy and a grade 12 girl? Explain your answer.

A stem-and-leaf plot is a way to organize data in order of place value. The “tens digit and greater” is the stem and the “ones digit” is the leaf. For example, in the data value 68, the 6 is in the tens place, so it is a stem. The 8 is in the ones place, so it is a leaf. A stem-and-leaf plot for 55, 68, 72, and 77 (written in ascending order) is:

Stem (tens)

Leaf (ones)

5 5 6 8 7 2 7

7. Create a stem-and-leaf plot for the male height data set. Arrange theleaves in ascending order.

Stem (tens) Leaf (ones)

8. Explain why a stem-and-leaf plot is a useful way to organize data.

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Math 3202 Section 2.1 Opening Investigation

Math 3202 Section 2.1 Mean, Median, Mode Notes

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Math 3202 Mean, Median, Mode

Sec 2.1 Mean, Median, and Mode

The mean, correctly called the arithmetic mean, is what people most often refer to as "average" in daily life. To find the arithmetic mean, add up the values in a data set and divide by the total number of values. is the math symbol that represents the mean.x

Example:

In real life, a weather reporter uses the mean to calculate the average temperature in a month.

You may calculate the average gas consuumption in your car.

Find the mean of the data set 4, 8, 9

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Example 1: Beatrice's soccer team scored the following number of goals in its last 10

games: 7, 2, 4, 7, 0, 1, 3, 2, 6, 1

What was the team's mean number of goals scored per game?

x = 3.3 goals/game

Example 2: In one game, a football team has offensive drives of 45 yd, 43 yd, 24 yd, 21 yd, and 44 yd. The coach wants the team to achieve a mean of 35 yd per drive for the game. What must the length of the next offensive drive be if the team wants to meet this goal?

The team's next offensive drive will have to be 33 yd to reach the desired average.

Example 3 Harpinder owns a store in Lethbridge, Alberta. He tracked his total sales for one week in the chart shown here. If the store is closed on Sunday, how much does he have to sell on Saturday for his mean sales to be $800.00 for each day his store is open?


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The median of a set of values is the midpoint of the data values when they are listed in ascending or descending order. Half the values are higher and half are lower than the median.

1, 3, 6, 8, 11, 14,16On an odd set of numbers, the median is the middle number of .

1, 3, 6, 8, 11, 14

With an even set of numbers, the median is the arithmetic mean of the two middle values . The median is

The median is often referred to when sales of houses are reported. The median selling price in a city tells you that half the houses sold at a higher price and half at a lower price.

Data could also be displayed in a stem and leaf plot. An odd-numbered set is shown below:

Stem Leaf1

2

3

4

5

6

7

8

9

2 2

1

2 2

6

3 3

8

3

1

The median or middle number is


In a list of values, the value that occurs most often is called the mode.

1, 2, 3, 4, 7, 2, 5, 8, 2, 6 Mode is

If each value occurs only once, there is no mode.

If two or more items appear the same number of times, then they are all considered modes.

1, 2, 12, 4, 7, 5, 8, 6 There is Mode

1, 2, 3, 6, 4, 7, 2, 5, 8, 2, 6, 7, 6

In workplace situations, mode is useful in several situations:* if you are a shoe manufacturer and you know that more women take a size 7shoe that any other size, you may use the mode to set your production run.

* If you manage a building supply store and your customers buy more 2" x 4"pieces of dimensional lumber than any other size, you will order your stock accordingly.

The Modes are

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A measure of central tendency refers to the middle of a distribution of data. The most common measure of central tendency are mean, median and mode. Look at the data plotted below. It shows the heart rate of a sample of 10 people. What are the mean, median, and mode of this data? How do these measures demonstrate the centre of the distribution of the data?

Example 4Barrie Gwillim operates a farm. He keeps meticulous records of his yield per acre for his different crops. One of the crops he has tracked is hard red spring wheat. The yields per acre from 2000 to 2010 are shown in the table below.

a) What is the mean yield of Barrie's crop per year?

b) What is the median yield of hard red spring wheatper year?

c) Does the data have a mode? If so, what is it?

d) Which measure of central tendency better represents Barrie's expected yields?Explain your reasoning.


Question 1

Alexis is a hair stylist. In one shift, she earned the following tips:

$5.00, $2.00, $0, $20.00, $19.65, $7.89, $8.50, $5.00

a) What is the mean tip Alexis received

b) What is the median?

c) What is the mode?

d) Which measure of central tendency best represents the average tip Alexisreceived?

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Measure of Central Tendency

Advantages Disadvantages

Mean

commonly used in familiar contexts

easy to calculate

useful when comparing sets of data

•

•

•

skewed by extreme values (outliers)

•

Median

extreme values do not affect this measure as strongly as they do the mean

• tedious to arrange large sets of data in order without technology

•

Mode

extreme values do not affect the mode

useful when the data values are limited in scope (e.g., shoe size)

can be used with non-numerical data sets (e.g., favourite color)

•

•

•

a set of data may have no mode

there may be more than one mode which can be diffi cult to interpret

•

•

Advantages and disadvantages of the measures of central tendency are shown below.

666 66

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A) D)Determine the mean.B) Identifyfthe outliers

1. 190, 210, 160, 250, 1,4400, 190

Mean =

Outlier:

2. 886, 77, 20, 81, 70, 86

IQuestion: Identify the outliers from each data set.

1. 38, 42, 77, 47, 74, 51, 48, 41, 82, 72, 74, 129 ____________________

Why?

2. 74, 63, 69, 62, 33, 79, 70, 60, 107, 119 __________________________

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Mean =

Outlier:

Why?

Outliers

Outliers: values that are significantly above or below the majority of the data


Question: Determine if there are any outliers in each set of data below.1. 65, 51, 47, 86, 88, 75, 66, 51, 88, 57, 69 YES/NO

2. 4, 2, 3, 5, -10, 1, 8, 2, 4, 6, 6, 7 YES/NO

3. 1000, 1000, 1002, 2098, 1500, 3000, 2500, 3000, 2001, 1092, 1200,1400, 2345, 3001 YES/NO

Question: Determine the outlier(s) in each of the following scatter graphs. Circle them on the graph.

Outlier:

Outliers:

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When people use an AVERAGE, they can use MEAN, MEDIAN, or MODE.

Which one is the one to use in each situation???

Example : An insurance company claims that the average age of drivers responsible for car accidents is 18. The data they used to get this average is shown below.

53 61 41 16 18 25 36 18 66 18 36

a) Find the:Mean:

Median:

Mode:

b) Which average did the insurance company use? Why do you think theywould choose to use this average?

c) Do you think this value best describes the data? If not, which valuedoes? Why?

Question 1: Calculate the mean, median and mode for each set of math test marks: Class 1: 80, 79, 93, 82, 88, 86, 90 Class 2: 79, 42, 93, 82, 88, 86, 90

Mean: Mean:

Median: Median:

Mode: Mode:

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Which average best represents each class?

Class 1: Class 2:

Question 2: Data: Amount of rain over the last seven days: 5 mm, 1mm, 0mm, 5mm, 1mm, 50mm, 5mm

Mean:

Median:

Mode:

Which average does not appear to be “in line” with the other values? Why is this?

What value is the outlier?

What happens when we remove the outlier?

Mean:

Median:

Mode:

An outlier can affect the mean causing the mean to no longer be a good measure off average.

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a) x ≈ $8.51b) median ≈ $6.45c) mode is $5.00d) The mean is not a good measure of central tendency for this data set. The mean of $8.51 is higher than all but two of the values in the data set. The median and the mode could both be good representations of Alexis's average tip.

Assignment Sec 2.1

Practice Your Skills

1. Manuel has trained as a flight attendant and is now looking for a job. Hehas researched the job market and has made the following list of the hourly pay at airlines in North America.

$22.45, $29.50, $22.40, $22.45, $28.75, $19.50, $17.45, $22.20$29.50, $22.45, $38.50, $16.65, $21.25, $22.20, $17.45, $21.15

a) Calculate the mean, the median, and the mode of the hourly pay rates.

b) Which measure is a better indicator of the salary Manuel might expect, andwhy?

2. Tristan owns a small garbage removal company. Last week, he made 12visits to the dump to empty his truck. He charged his customers the following amounts.

$450, $250, $375, $500, $125, $275, $75, $150, $375, $475, $200, $450

a) What was the mean amount Tristan charged his customers per load?

Name: __________________


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b) What was the median?

c) What was the mode? Explain whether or not this is a good measure of centraltendency.

d) Why would he have charged the customers different amount?

e) If it cost him $75 to dump each load:

i. how much did he make on the 12 loads?

ii. What were his mean earnings per load?

3. Frida calculates the statistics for a local baseball team in Iqalui, NU. Below arethe batting averages for 12 members of the team.

0.235, 0.324, 0.199, 0.256, 0.273, 0.301, 0.321, 0.224, 0.285, 0.185, 0.301, 0.209

a) Calculate the mean of the batting averages.


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b) Calculate the mode of the batting averages.

c) Calculate the median of the batting averages.

d) Which do you think is a better indicator of the batting average for the team?Why?

Samantha is a hairdresser at a busy salon in Mount Pearl, NL. Her customers often leave tips for her service. One afternoon, Samantha gave four haircuts and earned tips of $7.25, $6.50, $5.00, and $10.00. She is hoping to earn a mean amount of $7.50 in tips per haircut. If she has one more appointment scheduled for the day, ask students to determine how much she must earn from the tip to reach her goal.

4.

Julia and Marcus were both asked to determine the median of the following data set: 5, 8, 3, 14, 21, 16, 9, 18, 4Marcus stated that the median was 9 and Julia said it was 21. Which student is correct? Explain your reasoning.

5.


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An athete's sprint times are recorded for a one month period.

1. What is this athlete's mean time this month?

2. Is this mean higher or lower than you expectedfrom the numbers? Explain your thinking.

3. Are there any times that seem unexpected or irregular? Why do you think theyappear?

In the data table, sprints 5 and 9 are outliers: values that lie outside the normal range of the athlete's sprint times. How does including them in the calculations affect the mean time?

Try the calculations again, deleting these outliers. If you remove two highest outliers, you must remove the two lowest outliers to keep the data even. What is the new mean time?

Math 3202 Trimmed and Weighted Means and Outliers

Math 3202 Section 2.2 Trimmed and Weighted Means and Outliers Notes

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The mean found by omitting an equal number of values at the upper and lower ends of a data set is known as a trimmed mean. In the sprint data, you would disregard the two lowest values as well as the two highest values.

For a data set with outliers, the trimmed mean is a better measure of central tendency than the complete arithmetic mean.

Notice that the mean is now lower than the mean that was first calculated.

Another type of mean is a weighted mean, in which the values are assigned variable weights.

A teacher might calculate a weighted mean, making some assignments worth more than others.

For example, if you had three assignments and received grades of 65%, 95% and 80%, the arithmetic mean would be calculated as follows:

But what if the first and last assignments each counted for 40% of the final grade and the middle assignment only 20%? The weighted mean would then be calculated by multiplying each value by its percentage weight.

Weighted means are useful measures when the individual values have different levels of importance.


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Example 1Quillwork, the use of dyed porcupine quills to ornament practical and spiritual objects, was traditionally used by First Nations peoples including the Cree and Dene. Today, glass beads are more commonly used. Lois is a member of the Kehewin Cree nation in Alberta. She is well known for the colour combinations, designs, and fine workmanship of her beadwork. Lois makes note of how many hours she spends on each item she produces. This helps her calculate the object's price. Her hours spent on the last 10 purses she made are

6, 3, 8, 37, 9, 6, 8.5, 5, 7.5, and 9

a) What is the mean number of hours Lois spent on each purse?

b) What is the trimmed mean of hours spent on each purse?

c) Which seems like the more "average" number of hours spent on eachpurse, and why?

d) What might explain the outliers in this case?


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Example 2

A teacher has two grade 12 math classes. The 25 students in class A earned the following test results.

65%, 75%, 92%, 53%, 87%, 59%, 32%, 80%, 76%, 37%, 68%, 79%, 67%, 69%,

81%, 57%, 66%, 71%, 90%, 73%, 90%, 72%, 61%, 67%, 53%

a) What is the arithmetic mean for class A?

The 20 students in class B wrote the same test, and earned the test results below.

98%, 79%, 83%, 58%, 69%, 84%, 77%, 86%, 89%, 63%, 78%, 76%, 59%

89%, 74%, 55%, 69%, 64%, 87%, 98%

b) What is the arithmetic mean for class B?

c) Calculate the mean for the two classes combined.


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Example 3Francois is studying to become a paramedic in the Primary Care Paramedic program offered through the Justice Institute of British Columbia and Selkirk College in Trail, BC.

Francois earned the following marks:

8/10 on the first written assignment 7/10 on the first quiz7.5/10 on a presentation9/10 on the second written assignment 10/10 on the second quiz82% on the final exam

His final grade is calculated as follows:

*each written assignment is 5%.

* each quiz is worth 10%

*

the presentation is worth 20%*

What is Francois's final grade?

the final exam is worth 50%.


Example 4In her job as a server at a restaurant, Glenna earned 2 tips of $6.00, 3 tips of $8.00, 3 tips of $10.00, and 6 tips of $12.00Calculate the mean tips using 2 different methods.

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Section 2.2 Work Sheet: A New kind of Average

1. A data set contains the following numbers:125, 164, 183, 154, 132, 129, 524, 476, 165, 133

a. Calculate the arithmetic mean.

b. Identify any outliers if they exist and calculate the trimmed mean.

2. Calgary, AB, is known for its Chinook winds, warm winds that blow from the PacificOcean and that can raise the temperature significantly over a short period of time.The following table shows the daily high temperatures for one week in January,during which there was a Chinook wind.

a. What was the mean high temperature for the week?

b. On what day did the Chinook occur?

c. What is the trimmed mean of the daily highs?

d. Which is the better indicator of the expected daily high in Calgary for a weekin January? Why?

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3. Carina is calculating her final grade in her Spanish class. In the course, assignmentsare worth 15% all together, each quiz is worth 5%, the presentation is worth 25%,and the final exam is worth 45%. Carina earned:• 8/10, 6.5/10, and 16/20 on her

assignments• 85/100 on her presentation

• 10/10, 7/10, and 7/10 on herquizzes

• 86% on her final exam

What is Carina’s final grade?

4. The annual salaries for employees at Don’s Plumbing Store are:$15 000.00, $26 000.00, $29 000.00, $27 000.00, $60 000.00, $30 000.00

a. Calculate the mean salary.

b. Identify any outliers and calculate the trimmed mean.

c. Explain why there is a difference between the trimmed mean and thearithmetic mean.

5. Liviu is a real estate salesperson. He recently sold houses for the following prices:$289 000, $454 900,

$359 000, $376 500,

$1 356 000, $376 900, $425 800

a. Calculate the mean selling price.

202020

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b. Identify any outliers and calculate the trimmed mean.

c. Which calculation do you think best represents the average price of a housesold by Liviu?

6. Adi wrote three math tests each worth 20% of his final grade. He got marks of 75%,80%, and 86%. What mark must he get on the final exam (worth 40%) if he wants afinal grade of 86%?

7. Jeffrey sells computers and other equipment at an electronics store. He is compilingstatistics on the spending habits of customers. The table below shows customers’spending (rounded to the nearest $100.00).

What was the mean spending (rounded to the nearest dollar) per customer?

8. Calculate the arithmetic mean of the following set of numbers: 16, 16, 16, 18, 19, 19,20, 20, 20, 20, 20, 25, 25, 25, 25, 32, 32, 35, 35, 35, 35

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Math 3Math 3202 Section 2.2 Trimmed and weighted Means and Outliers Notes

9. Josh wants to know how many sports students in his school practice. He did asurvey and found that:• 25 students do 1 sport• 32 students do 3 sports

• 75 students do 2 sports• 5 students do 4 sports

What is the average number of sports practiced by a student in Josh’s school?

10. Luanne creates pottery that she sells at craft fairs around Saskatchewan. At onecraft fair, she sold:

• 5 items for $25.00 each• 6 items for $14.00 each• 12 items for $16.00 each

• 1 item for $45.00• 3 items for $21.00 each

10. 11. What is the mean cost per item Luanne sold?

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Assignment Sec 2.2

Practice Your Skills

Name: ______________

1. During the last six months, Arbit, a real estate agent, sold 9 housesfor the following prices:

$1 479 000 $750 000 $699 000 $435 900 $659 000

$589 500 $449 900 $625 600 $712 800

a) Would the arithmetic mean or the trimmed mean be a betterindication of the average price of a house he sold? Why? Calculate this value.

b) Which is higher, the trimmed mean or the arithmetic mean? Why?


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2. Jolene is an electrician. Her most recent job was at theCommunity Learning Centre in Hall Beach, NU. She installed three ground fault circuit interrupters at $40 each, six 3way switches at $62.50 each, forty 110volt outlets at $37.50 each, and two 220volt outlets at $47.50 each. What was the mean cost per installation?

3. Salima is studying in the Prairie Horticulture Program at BrandonManitoba's Assiniboine Community College. In her nursery crop production class, she earned the following grades: 75%, 81%, and 77% on three assignments; 65%, 90%, and 77% on three quizzes; and 81% on the final exam. Assignments are each worth 8% of the final grade, quizzes are each worth 12%, and the final exam is worth 40%. What was Salima's final grade?


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Math 3202 Section 2.2 Percentile Rank Notes

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Math 3202 Percentile Ranking

A percentile is a unit in a range of values divided into 100 equal parts, beginning at zero and ending at 100. Percentiles may be expressed by the numerals 1 to 99 but they are also often expressed in tens: 10 to 90.

For example, if you line up 100 people from shortest to tallest. You are the 91th person in line. That means that 9 people are taller and 90 people are shorter. You are in the 90th percentile for your height.

Percentiles are used to organize sets of data, such as test scores, so you can see how one score compares to others in the set.

Percentiles divide a distribution of data into two or more groups.

The 50th percentile corresponds to the the median value in a data set.

The 25th and 75th percentiles, representing the medians of the lower and upper halves of the data set respectively.

Also know as lower and upper quartile.

Example: Determine the 50th, 25th, 75th percentile for the data set: 71, 76,77, 34, 89, 54, 69, 94, 46, 72, 71, 88, 82, 63, 89, 45, 77, 81, 77, 75, 67, 67, 71, 89, 85, 58, 75, 52, 74

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A percentile rank tells you the percentage of values in a set of data that are lower than a given value. Perhaps you got a score of 8 out of 10 in a classroom quiz. Is that a good result? How would you know?

Consider the quiz scores marked on the line plot below. The quiz was out of 10 and the x's represent the number of students who earned each score.

0 1 2 3 4 5 6 7 8 9 10

xxx

xxxx

xx x

One student earned 10/10 on the quiz. What percentile ranking has this student obtained?

Look at the number of students who scored below 10/10. Nine students scored a lower number. Thus, 90% of the students scored less and the student earning 10/10 is in the 90th percentile.

0 1 2 3 4 5 6 7 8 9 10

xxx

xxxx

xx x

What is the percentile ranking for the student who earned 8/10?

Count the number of students who scored less the 8/10. There are 7.

To find the percentile rank, divide 7 by the total number of students and multiply by 100.

percentile ranking = x 100

percentile ranking = 70

710

The two students who scored 8/10 are in the 70th percentile and 70% of the students scored lower than they did.

Note that the percentile rank cannot be written as a percent.


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Percentile Ranking FormulabnPR = x 100

PR percentile ranking

b is the number of values below the one being considered

n is the total number of values in the data set.

Notice the percentile rank is not the percent score earned by the students.

The percentile rank tells you the percentage of students who scored less, not the percent score earned on the quiz.

What percentile rank would the top scorer have if his or her score was 9.5/10 rather than 10/10.Example 1

Great Canadian Insurance Company is evaluating the amount of coverage they offer for various services. They have collected the following data about the cost of a physiotherapy session at various clinics in Vancouver, BC.

$95 $66 $56 $50 $60 $60 $55 $55 $145 $140 $140 $75 $85 $90 $59

a) Calculate the percentile for $85

b) One way insurance companies decide how much to compensate theirclients for healthcare procedures is to use the 80th percentile of costs for the procedure within a geographic area. What is the cost of a session in the 80th percentile in Vancouver?


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Example 2

The salaries per month, rounded to the nearest $25, for the parttime workers in a department store are shown in the table below.

If Ellika earns $950, what is her percentile ranking?

Example 3Tom and Sarjit have just completed the Mortgage Brokerage course. There were 175 people in the class.

a) If 90 of the students scored lower than Tom in the course, what was hispercentile rank?

b) If 50 of the students scored higher than Sarjit and 3 people got the same scoreas him, what was his percentile rank?

c) What can you say about how Tom and Sarjit's scores compare to each other?


Jonathan Mauger

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Example 4Alexandre is the manager of a busy chain restaurant in Fort Nelson, BC. At the end of the month, the food sales of all the restaurant chain's locations in the province are compared to find out which location is the most successful. Out of 35 restaurants, Alexandre's restaurant is the only restaurant in the 20th percentile. How many restaurants were more successful than Alexandre's?


Check Your Understanding Page 90 Questions # 5 b, c, d, 6, 7Work With it Page 91 Questions # 2

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Assignment 2.2

Build Your Skills

Name: _______________

1. As part of the graduation committee, Marija orders the graduationgowns for a class of 152 students. She knows that her percentile ranking for height is 75 and that 7 others are the same height as her. How many students are taller than Marija?


2. In a report on electricians' salaries in different companies, thefollowing data were recorded.

If Javier works for company B, what is his percentile ranking with respect to wages?

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3. Karl got 32 out of 93 on a test. Of the 223 people who wrote the test,14 earned the same score as Karl, and 73 scored higher than he did.

a) What was Karl's percentile rank?

b) What percentage of the questions did he get correct?

c) Are your answers to a) and b) the same? What might this tell you?


Unit 2: Working With Data Explore Scatter Plots Activity

1. Working with a partner, measure and record the length of your forearmand your hand span to the nearest millimetre.

2. Collect the same data from all the members of your classand record it in the table below.

3. Graph the pairs of data for each person.

Forearm Length (mm) Hand Span (mm)

Math 3202 Section 2.3 Scattered Plots

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A1

4. a) Describe a trend represented by the graphed data.

b) Do the points graphed form a straight line?

5. a) From the graph, can you predict the hand span of a person whose forearm length is beyond the longest forearm length? Why or why not? This is called extrapolating.

b) Can you predict the hand span of a person whose forearm length isbetween two given forearm lengths? This is called interpolating.

6. Does plotting both genders on the same graph affect the trend? Why or whynot?

Math 3202 Section 2.3 Scattered Plots

A2

Scatter Diagrams

Correlation =

Types of Correlations

1. Positive correlation –

2. Negative correlation -

3. No correlation –

As you get heavier, your height usually _________________________.

As you spend more time at home, you spend _______________________ at work.

The number of the classroom number you are in has nothing to do with your house number.

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Math 3202 Section 2.3 Scattered Plots Notes

Correlations can be strong or weak. A strong correlation means that all the data are close to a

_________________line.

A weak correlation means that the points are _________________line.

Lines of Best Fit

Only drawn when there is a _______________________________ The line of best fit is drawn through, or close to, as many points as possible.

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Lines of Best Fit

Only drawn when there is a correlation The line of best fit is drawn through, or close to, as many points as possible.


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Example 2

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Interpolation is the prediction of a value between two known values.

Extrapolation is the prediction of avalue which goes beyond the data that is given.

Worksheet Section 2.3 Scatter Graphs – Lines of Best Fit and Making Predictions

1. a) Draw a scatter graph for the data below. Math mark goes along the

horizontal axis, physics mark along the vertical axis. Label the axes.

Math (%) 56 24 67 70 71 42 48 32 52 80 Physics (%) 65 38 71 72 73 51 56 42 57 82

20 40 60 80 100

20

40

60

80

100

b) Draw a line of best fit for this data.

c) What type of correlation is this? (positive, negative, none) (weak,strong) __________________________________

d) What does the graph tell us about the relationship between math marksand physics marks? Finish the sentence.

If the math mark increases then the physics mark _______________.

e) One student scored 65% on their Math exam. Predict what they scoredin Physics using the line of best fit. Show work on graph.

_________________

Is this interpolation or extrapolation? (circle)

g) A student got 39% on their Physics exam. What was their predictedmark in math? Show work on graph. _________________


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2. a) Draw a scatter graph for the data below. Science mark goes along the horizontal axis, history marks along the vertical axis. Label the axes.

Science (%) 15 63 18 34 44 50 25 54 85 29 39 74 History (%) 72 38 72 58 52 50 66 44 19 63 54 28

20 40 60 80 100

20

40

60

80

100


c) What type of correlation is this?

___________________________________

d) What does the graph tell us about the relationship between sciencemarks and history marks? Write a sentence.

e) One pupil scored 60% in the Science exam. What do you think they goton their History exam? (use line of best fit). ____________________ Is this interpolation or extrapolation? (circle)

f) One pupil scored 60% on their History exam. Predict what they got inscience. ______________________ Is this interpolation or extrapolation? (Circle)

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Check Your Understanding Page 99 Questions # 5, 6Work With It Page 101 Questions # 4,5

1. a) Draw a scatter graph for the data below. Rainy days is the independent variable and sunny days the dependent variable. IGNORE THE MONTH – it is extra information. Label the axes.

Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Rainy Days 10 15 18 10 4 10 1 0 5 5 10 14

Sunny Days 6 4 8 10 18 16 20 25 19 16 14 12

5 10 15 20 25 30

5

10

15

20

25

30



__________________________________

d) If there was 25 rainy days, how many sunny days would you expect?(use line of best fit)

________________________________

e) Is this interpolation or extrapolation? (circle)

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Assignment: Section 2.3

Name: __________________

2. a) Draw a scatter graph for the data below. Paris temperature is the independent variable. Madrid temperature is the dependent variable. Label the axes.

Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Paris Temp (‘C) 4 4 7 10 14 17 19 19 16 13 7 5

Madrid Temp (‘C) 5 7 10 12 16 21 25 24 21 15 9 6

5 10 15 20 25 30

5

10

15

20

25

30



_________________________________

d) What does the graph tell us about the relationship between thetemperature in Paris and the temperature in Madrid? Write a sentence.

e) If the temperature in Madrid was 18, what would you expect thetemperature to be in Paris? (use line of best fit).

__________________________________


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Math 3202 Section 2.1 Opening Investigationmrmcdonaldshomepage.weebly.com/uploads/1/3/9/2/13921997/mat… · Math 3202 Section 2.1 Opening Investigation: Math 3202 Section 2.1 Mean,