Central Tendency’s

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! Family Name# of members Mr. Unreiner4 Mrs. Sas11 Mr. Aberle13 Mr. Bosch6 Mr. Gans3 Mr. Siedlecki4 Mr. Lanigan8

12.1 Place the numbers in order… Student Outcome: I will learn and solve problems using central tendency’s. Raw Data Ordered Data 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 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 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.Odd #’s: 2.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 = 26 The median is = _______ The mode is = _______ The mean is = _______ PROBLEM: Find the median, mode and mean price for the total number of shirts sold! You may work with a partner. What is the mode (most often)?

Median (Ordered data) 8,8,8,8,8,8,14,14,14,14,14,14,14,17,17,17,17, 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 = _____ PROBLEM: Find the median, mode, mean price for the number of coffees sold. 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

Example #1 The data below are the yearly wages (in dollars) of ten people working at an on-line music store. DATA: { , , , , , , , , , } 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 ,13,14,15,16 113,6,10,12 3,6,7,10 SHOW YOUR WORK!!!

Show Me What You Know#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: Mean = = 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 Mean = ______ Mean = ______

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 Total Chip Sales Monday140 Tuesday90 Wednesday80 Thursday90 Friday110 Saturday120 Are there any days that the stores has sales below the mean? SHOW YOUR WORK

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 $100/dayTotal Chip Sales Monday Tuesday10090 Wednesday10080 Thursday10090 Friday Saturday Sunday100

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 Dist. Travelled (km.) Monday44 Tuesday52 Wednesday51 Thursday46 Friday57 SHOW YOUR WORK Find the mean…

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.

Central Tendency’s nhl-hockey nhl-hockey

12.2 Practice makes Perfect! Page ,15,16 112,7,9,12 2,5,7,10 SHOW YOUR WORK!!!

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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: RangeMedianModeMean

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: RangeOutliers 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. Top NHL Scorer SeasonPoints SeasonPoints Wayne Gretzky215Joe Thornton125 Mario Lemieux141Jaromir Jagr123 Paul Coffey138Alexander Ovechkin106 Jari Kurri131Dany Heatly103 Mike Bossy123Daniel Alfredsson103 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. Top NHL Scorer SeasonPoints SeasonPoints Wayne Gretzky215Joe Thornton125 Mario Lemieux141Jaromir Jagr123 Paul Coffey138Alexander Ovechkin106 Jari Kurri131Dany Heatly103 Mike Bossy123Daniel Alfredsson103 1.Find the ranges for both seasons? How do they compare? = 92 and = 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. Top NHL Scorer SeasonPoints SeasonPoints Wayne Gretzky215Joe Thornton125 Mario Lemieux141Jaromir Jagr123 Paul Coffey138Alexander Ovechkin106 Jari Kurri131Dany Heatly103 Mike Bossy123Daniel Alfredsson103 1.Find the ranges for both seasons? How do they compare? = 92 and = 22 2.Which data value appears to be an outlier in one of the two seasons? Season 3.Remove the outlier and determine the new range. Now, how do the two season ranges compare?

12.3 Practice makes Perfect! Page ,15,16 123,6,9,16 2,5,6,8,9 SHOW YOUR WORK!!!

Show Me What You Know#3

12.4 The 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). StudentKennedyLoganMarkDaraghSamEvanMorgan Length (cm) 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. 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. 2. Then find the measures of central tendencies.

12.4 The Effects of Outliers! Student Outcome: I can identify/explain effects of outliers for sets of data. StudentKennedyLoganMarkDaraghSamEvanMorgan Length (cm) 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: 2.7 Range: 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 = = 5.5/2 = 2.75

12.4 Practice makes Perfect! Page ,7,8 51,4,6 1,3,4 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 = 8 Mode = 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? DateSept Oct Nov Sales 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? DateSept Oct Nov Sales What are the mean, median, mode and range? Mean: 130/10 = 13.0 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? DateSept Oct Nov Sales Share your answers with a classmate. Do you agree…if not, explain the reasons for your selection. Mean: 13 Median: 9 Mode: 7 4. How many T-shirts should be purchased for the next 30 weeks? Explain.

12.5 Practice makes Perfect! Page ,12,14,15 93,6,8,10 2,3,6,7 SHOW YOUR WORK!!!

Chapter “9-12” Review Page #1-22 SHOW YOUR WORK!!!

Math Game – Page 456

Analyze Your Survey This is a summary assignment where you will create a survey and analyze the data. You will create a question to survey the entire class of 7-1. Things to do… 1. Create a survey question with choices. 2. Create a tally chart to record data.

Survey Question What is your favorite chips? ◦ Ketchup ◦ BBQ ◦ Salt + Vinegar ◦ All Dressed ◦ Sour Cream ◦ Plain ◦ Other

Tally Chart Type of Chips Amount of People (Tally) Frequency KetchupIIII5 BBQIII3 Salt + Vinegar 0 All DressedI1 Sour CreamIIII5 PlainIIII 10 OtherIIII I6

Analyze Your Data… 1. Analyze your data to help you decide what you need to order. Include measure of central tendency(mode, median, mean), range, outliers (include or delete?). 2. Summarize and explain which measure of central tendency is most reasonable. 3. Make two inferences (interpretations) about your data? What do you notice?

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! Things to do… 1. What sizes to order (ages 12-14)? 2. What brand names to order? 3. How much are teenagers willing to pay?

Your own “Shoe Store” What sizes to order??? Ask 20 friends/family… Shoe SizeAmount of People (Tally)

Your own “Shoe Store” What brand to order??? Ask the same 20 friends/family… Think of at least 10 different brands Shoe BrandAmount of People (Tally) DC Adidas Nike Gravis

Your own “Shoe Store” What price are they willing to pay??? 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! Shoe BrandAmount of People (Tally)

Your own “Shoe Store”

Analyze Your Data… 1. 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.