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Central Tendency’s

Central Tendency’s. https:// www.youtube.com/watch?v=5C9LBF3b65s. Working With DATA … ( Unit 12 ) Student Outcome: I will learn and solve problems using central tendency’s.

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Central Tendency’s

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  1. Central Tendency’s • https://www.youtube.com/watch?v=5C9LBF3b65s

  2. 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) 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!

  3. 12.1 Place the numbers in order…Student Outcome: I will learn and solve problems using central tendency’s. Raw Data6 4113 8 134 Ordered Data3 4 4 6 8 11 13 Measure of Central Tendency: The value that represents the centre of a set of data… • Median: the middle number of the data = ___________ • Mode: the number that occurs the most = ___________ • Mean: the average of all the numbers…add all the numbers and then divide them by the amount of numbers = __________

  4. 12.1 Try it again…(Median)Student Outcome: I will be able to determine the median of a data. Raw Data4 8 6 2 9 4 11 7 Ordered Data Increasing order is called: • The median is = _______ • The modeis = _______ • The meanis = _______ What is the mode (most often)?

  5. 12.1 Try it again…(Median)Student Outcome: I will be able to determine the median of a data. Raw Data8 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 modeis = _______ • The meanis = _______ • RULE: for finding the median. Can you come up with one? • Odd #’s: • Even #’s: What is the mode (most often)?

  6. 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 price for the total number of shirts sold! You may work with a partner. • The median is = _______ • The modeis = _______ • The meanis = _______ What is the mode (most often)?

  7. 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

  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 for the number of coffees sold. • The median is = _______ • The modeis = _______ • The meanis = _______

  9. 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

  10. 12.1 TRY ANOTHER ONE… Learn Alberta – mode, median http://www.learnalberta.ca/content/memg/index.html?term=Division03/Mode/index.html

  11. 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?

  12. 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?

  13. 12.1Practice makes Perfect! Page 426-427 3,13,14,15,16 113,6,10,12 3,6,7,10 SHOW YOUR WORK!!!

  14. Show Me What You Know#1

  15. 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

  16. 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 7 8 3 6 2 1 • Mean = ______

  17. 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? • Are there any days that the stores has sales below the mean?

  18. 12.2Tricky 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?

  19. 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. • Find the mean…

  20. 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: • Predict how many kilometres the salmon will travel on Saturday? • Predict how many kilometres the salmon will travel over… • 8 days? • 12 days? • 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.

  21. 12.2 TRY ANOTHER ONE… Learn Alberta – mean http://www.learnalberta.ca/content/memg/index.html?term=Division03/Mode/index.html

  22. 12.2Practice makes Perfect! Page 431-432 9,15,16 112,7,9,12 2,5,7,10 SHOW YOUR WORK!!!

  23. Show Me What You Know#2

  24. 12.3Range&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

  25. 12.3Range&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 5 9 4 7 11 • Outliers • Range In your own words explain how you can determine whether there is an outlier in a set of data

  26. 12.3Identify Outliers to find a “New Range”Student Outcome: I will determine the range and outliers from sets of data. • Top NHL Scorer • Find the ranges for both seasons? How do they compare?

  27. 12.3Identify Outliers to find a “New Range” Student Outcome: I will determine the range and outliers from sets of data. • Top NHL Scorer • Find the ranges for both seasons? How do they compare? 1985-86 = 92and 2005-06 = 22 • Which data value appears to be an outlier in one of the two seasons?

  28. 12.3Identify Outliers to find a “New Range”Student Outcome: I will determine the range and outliers from sets of data. • Top NHL Scorer • Find the ranges for both seasons? How do they compare? 1985-86 = 92and 2005-06 = 22 • Which data value appears to be an outlier in one of the two seasons? 1985-86 Season • Remove the outlier and determine the new range. Now, how do the two season ranges compare?

  29. 12.3 TRY ANOTHER ONE… Learn Alberta – mean http://www.learnalberta.ca/content/memg/index.html?term=Division03/Mode/index.html

  30. 12.3Practice makes Perfect! Page 437-439 3,15,16 123,6,9,16 2,5,6,8,9 SHOW YOUR WORK!!!

  31. Show Me What You Know#3

  32. 12.4The Effects of Outliers!Student Outcome: I can identify/explain effects of outliers for sets of data. Be able to “justify” whether outliers should be included when determining measures of tendency (mean, mode, median & range). 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. • 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.

  33. 12.4The Effects of Outliers!Student Outcome: I can identify/explain effects of outliers for sets of data. • 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: 2.7Range: 3.2 – 2.4 = +0.8 • Mean: 16.9/ 6= 2.816 = 2.8 • Median: 2.4, 2.7, 2.7, 2.8, 3.1, 3.2 = 2.7 + 2.8 = 5.5/2 = 2.75

  34. 12.3 TRY ANOTHER ONE… Learn Alberta – central tendancy’s http://www.learnalberta.ca/chttp://www.explorelearning.com/index.cfm?method=cExtAccessSecure.dspResource&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

  35. 12.4Practice makes Perfect! Page 444-445 6,7,8 51,4,6 1,3,4 SHOW YOUR WORK!!!

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