Transcript Slide 1
Working With
DATA
… ( Unit 12 )
Student Outcome: I will learn and solve problems using central tendency’s.
Before you can find the median, mode, mean, range or outliers you must always
ORDER
your data in correct order from lowest to highest of numbers ( a.k.a. = increasing order or ascending )
Family Name # of members
Mr. Unreiner 4
Example
: Here is a list of families that have different amounts of people in their family. You must organize your data from lowest to highest numbers first!
Mrs. Hintz Mr. Aberle Mr. Bosch Mr. Gans Mr. Siedlecki Mr. Lanigan 4 8 6 3 11 13
12.1
Place the numbers in order…
Student Outcome: I will learn and solve problems using central tendency’s.
Raw Data 6 4 11 3 8 13 4 Ordered Data 3 4 4 6 8 11 13 Measure of Central Tendency
: The value that represents the
centre
of a set of data… 1. Median : the middle number of the data = ___________ 2. Mode : the number that occurs the most = ___________ 3. Mean: the average of all the numbers…add all the numbers and then divide them by the amount of numbers = __________
12.1
Try it again…(Median)
Student Outcome: I will be able to determine the median of a data.
Raw Data 4 8 6 2 9 4 11 7 Ordered Data Increasing order
is called: The
median
is = _______ The
mode
is = _______ The
mean
is = _______
What is the mode (most often)?
12.1
Try it again…(Median)
Student Outcome: I will be able to determine the median of a data.
Raw Data 8 9 5 7 2 5 4 11
Remember…place them into increasing order first! Then find the middle number.
Ordered Data
The
median
is = _______ The
mode
is = _______ The
mean
is = _______
RULE
: for finding the median. Can you come up with one?
1.
2.
Odd #’s: Even #’s:
What is the mode (most often)?
12.1
TRICKY QUESTION…
Student Outcome: I will be able to determine the median of a data.
The total number of T-shirts sold are 6 + 7 + 5 + 4 + 4 =
26 PROBLEM:
Find the median, mode and mean may work with a partner.
price
for the total number of shirts sold! You The
median
is = _______ The
mode
is = _______ The
mean
is = _______
What is the mode (most often)?
Median (Ordered data) 8,8,8,8,8,814,14,14,14,14,14,14,17,17,17,17, 17,20,20,20,20,25,25,25,25 Mode: Mean = 411 ÷ 26 = 15.8
12.1
TRY ANOTHER ONE…
Student Outcome: I will be able to determine the median of a data.
The total number coffees sold.
12 10 9 5 = _____
PROBLEM:
Find the median, mode, mean
price
the number of coffees sold.
for The
median
is = _______ The
mode
is = _______ The
mean
is = _______
Median (Ordered data) 2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3.5, 3.5,3.5,3.5,3.5,3.5,3.5,3.5,3.5,4,4,4,4,4 Mode: Mean = 105.5÷ 36= 2.9
12.1
TRY ANOTHER ONE…
Learn Alberta – mode, median http://www.learnalberta.ca/content/memg/index.html?term=Division03/Mode/index.html
Example #1
The data below are the yearly wages (in dollars) of ten people working at an on-line music store.
DATA: { 41 000, 41 000, 41 000, 41 000, 43 000, 45 000, 48 000, 50 000, 50 000, 250 000 } What is the: Mean Median Mode Based on the data what “inferences” can you make?
Example #2
The data below are the seventeen shoe sizes of one type of shoe sold in one day at a local shoe store.
DATA: { 5, 6, 7, 7, 7, 7, 7, 7, 8, 9, 9, 10, 11, 12, 13, 13, 15 } What is the: Mean Median Mode Based on the data what “inferences” can you make?
12.1
Practice makes Perfect!
Page 426: # 4, 6, 7 Page 427: # 10, 11, Extend #13, 14a, 17
SHOW YOUR WORK!!!
Practical Quiz #1
12.2
Finding the “ MEAN ”
Student Outcome: I will be able to determine the mean of a data.
Mean: the sum of a set of values divided by the number of values in the set.
Example: 4 5 9 11 6 8 Mean = 4 + 5 + 9 + 11 + 6 + 7 6 = 7
12.2
Finding the “ MEAN ”
Student Outcome: I will be able to determine the mean of a data.
Find the mean to the values in the sets below.
12 14 8 6 23 Mean = ______ 4 6 Mean = ______ 7 8 3 6 2 1
12.2
Calculate the mean of sales!
Student Outcome: I will be able to determine the mean of a data.
What is the daily mean number of sales from Monday to Saturday?
Days of The Week
Monday
Total Chip Sales
140
SHOW YOUR WORK
Tuesday Wednesday Thursday Friday Saturday 90 80 90 110 120
Are there any days that the stores has sales below the mean?
12.2
Tricky Question …
Student Outcome: I will be able to solve problems using the mean.
Let’s say the daily mean of sales was 100 for 7 days (a full week). How many chips would you need to sell on Sunday? How do you solve this?
Days of The Week
Monday Tuesday Wednesday Thursday Friday Saturday Sunday 100 100 100 100
$100/day Total Chip Sales
100 140 100 100 90 80 90 110 120
12.2
Use the mean to “ PREDICT ”
Student Outcome: I will be able to solve problems using the mean.
A scientist recorded the daily distance travelled by a spawning salmon for five days.
Days of The Week
Monday
Dist.
Travelled (km.)
44
Find the mean …
Tuesday 52
SHOW YOUR WORK
Wednesday Thursday 51 46 Friday 57
12.2
Use the mean to “ PREDICT ”
Student Outcome: I will be able to solve problems using the mean.
Now that you know the average (mean) distance travelled is 50km…find some predictions.
Predictions : 1.
Predict how many kilometres the salmon will travel on Saturday ?
2.
• •
Predict how many kilometres the salmon will travel over… 8 days?
12 days?
3.
A Chinook Salmon may travel 8000km from its feeding grounds in the North Pacific Ocean. Use your mean to find out how many days it will take for this fish to travel.
12.2
TRY ANOTHER ONE…
Learn Alberta – mean http://www.learnalberta.ca/content/memg/index.html?term=Division03/Mode/index.html
Practical Quiz #2
12.2
Practice makes Perfect!
Page 431: # 3, 5, 7 Page 432: # 8,10, 14 SHOW YOUR WORK!!!
12.3
Range & Outliers …
Student Outcome: I will determine the range and outliers from sets of data.
Range: The positive difference between the largest & smallest values in a set of data.
Example: 4 5 9 11 6 8 13 22 5 Range Median Mode Mean
12.3
Range & Outliers …
Student Outcome: I will determine the range and outliers from sets of data.
Outliers: A value that is MUCH smaller or larger than the other data values…might be one or more or none !
Example: 3 10 67 8 Outliers Range 5 9 4 7 11
In your own words explain how you can determine whether there is an outlier in a set of data
12.3
Identify Outliers to find a “ New Range ” Student Outcome: I will determine the range and outliers from sets of data.
1985-1986 Season
Wayne Gretzky Mario Lemieux Paul Coffey Jari Kurri Mike Bossy
Top NHL Scorer Points 2005-2006 Season
215 Joe Thornton 141 138 131 123 Jaromir Jagr Alexander Ovechkin Dany Heatly Daniel Alfredsson
Points
125 123 106 103 103 1. Find the ranges for both seasons? How do they compare?
12.3
Identify Outliers to find a “ New Range ” Student Outcome: I will determine the range and outliers from sets of data.
1985-1986 Season
Wayne Gretzky Mario Lemieux Paul Coffey Jari Kurri Mike Bossy
Top NHL Scorer Points 2005-2006 Season
215 Joe Thornton 141 138 131 123 Jaromir Jagr Alexander Ovechkin Dany Heatly Daniel Alfredsson
Points
125 123 106 103 103 1. Find the ranges for both seasons? How do they compare? 1985-86 = 92 and 2005-06 = 22 2. Which data value appears to be an outlier in one of the two seasons?
12.3
Identify Outliers to find a “ New Range ” Student Outcome: I will determine the range and outliers from sets of data.
1985-1986 Season
Wayne Gretzky Mario Lemieux Paul Coffey Jari Kurri Mike Bossy
Top NHL Scorer Points 2005-2006 Season
215 Joe Thornton 141 138 131 123 Jaromir Jagr Alexander Ovechkin Dany Heatly Daniel Alfredsson
Points
125 123 106 103 103 1. Find the ranges for both seasons? How do they compare?
1985-86 = 92 and 2005-06 = 22 2. Which data value appears to be an outlier in one of the two seasons? 1985-86 Season 3. Remove the outlier and determine the new range. Now, how do the two season ranges compare?
12.3
TRY ANOTHER ONE…
Learn Alberta – mean http://www.learnalberta.ca/content/memg/index.html?term=Division03/Mode/index.html
Practical Quiz #3
12.3
Practice makes Perfect!
Page 437: # 3, 5, 7, 8
Page 438
: # 9, 12, 15 Page 439: # 16 (work with a partner on this one…good luck) SHOW YOUR WORK!!!
12.4
The Effects of Outliers!
Student Outcome: I can identify/explain effects of outliers for sets of data.
Be able to “ range).
justify
” whether outliers should be included when determining measures of tendency (mean, mode, median &
Example
: In a science class students were asked to take home a bean seed and to bring it back in two weeks. Below are the growth (height) results. 1.
2.
Is there and outlier and if so why should it be taken out of the class results? Give an explanation of what may have happened.
Then find the measures of central tendencies.
Student
Length (cm) Kennedy 3.2
Logan 2.7
Mark 3.1
Daragh 2.8
Sam 2.7
Evan 31 Morgan 2.4
12.4
The Effects of Outliers!
Student Outcome: I can identify/explain effects of outliers for sets of data.
Student
Length (cm) Kennedy 3.2
Logan 2.7
Mark 3.1
Daragh 2.8
Sam 2.7
Evan 31 Morgan 2.4
1. Is there and outlier and if so why should it be taken out of the class results? Yes there is an outlier… • • • Student may have measured in mm instead of cm.
Evan works at a greenhouse and placed steroids in the soil.
…share others!
2. Then find the measures of central tendencies.
Mode : there are none!
Range: 3.2 – 2.4 =
+0.8
Mean : 16.9
/ 6 = 2.8 Median: 3.2 2.7 3.1 2.8
3.1
+ 2.8
2.7 2.4
= 5.9
/2 =
2.95
12.3
TRY ANOTHER ONE…
Learn Alberta – central tendancy’s http://www.learnalberta.ca/chttp://www.explorelearning.com/index.cfm?method=cExtAccessSecure.ds
pResource&ResourceID=1018&certificate=authorizer%3DLearnAlberta%26userid%3DLA38%26i%3D0 %26expires%3D2011%252F05%252F31%2B14%253A52%253A53%26hash%3DuzBIC8kuNGpWU9NPn% 252Bj3iw%253D%253Dontent/memg/index.html?term=Division03/Mode/index.html
12.4
Practice makes Perfect!
Page 444: # 3, 5 Page 445: # 7 SHOW YOUR WORK!!!
12.5 “ BEST ” measure of central tendency Student Outcome: I will be able to solve problems using various types of central tendency’s How do you know when to use the mean, mode, median or range?
Taylor kept track of her quizzes for the week (4, 5, 8, 9, 9)… Median Mode = 8 = 9 Mean = 7 Which central tendency best describes her quiz results for the week?
12.5
Choose the “ BEST ” measure of central tendency
How do you know when to use the mean, mode, median or range?
Date Sales Sept 7 Sept 50 Sept 8 Oct 9 Oct 10 Oct 12 Oct 7 Oct 7 Nov 9 Nov 11 • • • 1. What are the mean, median, mode and range?
Mean: Mode: Median:
2. Compare the mean, median and mode. Which measure seems to best represent the ten numbers? Explain.
12.5 “ BEST ” measure of central tendency Student Outcome: I will be able to solve problems using various types of central tendency’s How do you know when to use the mean, mode, median or range?
Date Sales Sept 7 Sept 50 Sept 8 Oct 9 Oct 10 Oct 12 Oct 7 Oct 7 Nov 9 Nov 11 • • • 1. What are the mean, median, mode and range?
Mean: 137/10 = 13.7 which is rounded to “14 sales.” Mode: 7,7,7,8,9,9,10,11,12,50 = 7 is the most often Median: 7,7,7,8, 9,9 ,10,11,12,50 = 9…both the same #.
2. Compare the mean, median and mode. Which measure seems to best represent the ten numbers? Explain.
12.5 “ BEST ” measure of central tendency Student Outcome: I will be able to solve problems using various types of central tendency’s How do you know when to use the mean, mode, median or range?
Date Sales Sept 7 Sept 50 Sept 8 Oct 9 Oct 10 Oct 12 Oct 7 Oct 7 Nov 9 Nov 11 3. Share your answers with a classmate. Do you agree…if not, explain the reasons for your selection.
Mean: 14 Median: 9 Mode: 7 4. How many T-shirts should be purchased for the next 30 weeks? Explain.
12.5
Practice makes Perfect!
Page 449: # 3 Page 450: # 4, 6, 9 SHOW YOUR WORK!!!
Chapter
“9-12”
Review
Page 458-460 #
1-22
SHOW YOUR WORK!!!
Math Game – Page 456
Challenge In Real Life! – Page 457
This is a summary assignment where you will create a poster that indicates your investigation into size, brand and price of shoes for clients of your own age. Show ALL YOUR WORK !
1.
2.
3.
Things to do … What sizes What brand to order (ages 12-14)?
names to order?
How much are teenagers willing to pay?
Your own “Shoe Store”
What sizes to order???
Ask 20 friends/family…
Shoe Size Amount of People (Tally)
6 6.5
7 7.5
8 8.5
9
Your own “Shoe Store”
What brand to order???
Shoe Brand
Ask the same 20 friends/family… DC Adidas Nike Gravis
Amount of People (Tally)
Think of at least 10 different brands
Your own “Shoe Store”
What price are they willing to pay???
Shoe Brand
Ask the same 20 friends/family… Make sure to use the prices of the shoes mentioned…but don’t let them know which shoes cost which price!
20 30 40 50 60 70
Amount of People (Tally)
Your own “Shoe Store”
1.
Analyze Your Data…
Analyze your data to help you decide what you need to order. Include measure of central tendency for all three charts…make sure to take remove outliers…but make sure to mention them in your work!
2.
Summarize all three charts and explain which measure of central tendency is best for each. Be sure to explain your choices.
3.
You have 1 week to complete.