Topic Mean Median Mode EQ How do measures

Topic: Mean, Median, Mode EQ: How do measures of central tendency lead to different interpretations of the data? 1. -6 x – 5(x – 5) = 102 x = -7 3) Convert 17. 8 ft/hour to in/day 5, 126. 4 2) 7(6 - 8 m) = 210 m = -3

Hook Normal Weight • The CDC's weight-for-age graph lists the average weight of a 15 -year-old boy at 126 pounds. The chart shows that children weighing 172 pounds score in the 95 th percentile, or weigh more than 95 percent of boys their age. On the bottom end, boys weighing only 90 pounds fall in the 3 rd percentile. • For girls, the average weight is 114 pounds. Girls at 86 pounds fall to the low end of the measurement scale, in the 3 rd percentile. The 95 th percentile of girls at age 15 is 168 pounds, meaning that they weigh more than 95 percent of girls nationwide.

Hook Normal Height • The stature-for-age percentiles track the normal height for boys and girls. The average boy's height is 67 inches, or 5 feet 7 inches tall. Boys at 72 1/2 inches tall, or 6 feet and a 1/2 -inch, are taller than 97 percent of all other boys in America, while those at 61 inches fall into the 3 rd percentile. For girls, 64 inches, or 5 feet 4 inches tall, is considered a normal height. To fall within the 97 th percentile, a 15 -yearold girl needs to only be 69 inches tall. A 59 -inch tall --- or 4 feet 11 inches --- girl is in the 3 rd percentile for height. Read more: http: //www. livestrong. com/article/370690 -theaverage-weight-height-of-a-15 -year-old/#ixzz 2 bt. EXFz. PD

Measures of Central Tendency Objective: SWBAT compute the measures of central tendencies of a data set (mean, median, and mode) (3. 1. a. ii) D. O. L. : Students will be able to calculate the 3 measures of central tendency and rationalize which is the most appropriate. Why - A measure of central tendency describes how data clusters around a value. For example, you may receive various test scores on each unit exam throughout the semester. You can condense these values into one single score that represents your math knowledge.

Essential Question • How do various measures of central tendency lead to different interpretations of the data?

The Iditarod 9 13 Winning Times (days) 19 9 11 18 14 15 13 9 Think Pair Share Which number appears most often? 9 If you list the data in order from least to greatest, which number is in the middle? 13

The Iditarod 9 13 Winning Times (days) 19 9 11 18 14 15 13 9 Think Pair Share What is the sum of all numbers divided by 10? 13 If you had to give one number that best represents the winning times, which would you choose? Explain

Measures of Central Tendency • Mean (Average) – To find: Add up the values, divided by the number of values – Use when there are no outliers • Median – To Find: Middle number in a list from least to greatest • When there are two, find the average (sum and divide by 2) – Use when there is an outlier • Mode – To Find: Most popular or most frequently occurring number • Only use when the values are non-numeric

Find the Mean, Mode, and Median • According to “The Internet Movie Database”, the following movies are the biggest grossing movies of all time. Top Ten Movies and Revenue (millions) - 2008 Titanic 600 The Dark Knight 533 Star Wars 460 Shrek 2 436 E. T. 434 Star Wars Episode I – Phantom Menace 431 Pirates – Dead Man’s Chest 423 Spider Man 402 Transformers – Revenge of the Fallen 402 Star Wars Episode III – Revenge of the Sith 380

Find the Mean, Mode, and Median • Find the Mean. 450. 1 • Make this easy by rounding each value. Top Ten Movies and Revenue (millions) - 2008 Titanic 600 The Dark Knight 533 Star Wars 460 Shrek 2 436 E. T. 434 Star Wars Episode I – Phantom Menace 431 Pirates – Dead Man’s Chest 423 Spider Man 402 Transformers – Revenge of the Fallen 402 Star Wars Episode III – Revenge of the Sith 380

Find the Mean, Mode, and Median • Find the Mode is 402 Top Ten Movies and Revenue (millions) - 2008 Titanic 600 The Dark Knight 533 Star Wars 460 Shrek 2 436 E. T. 434 Star Wars Episode I – Phantom Menace 431 Pirates – Dead Man’s Chest 423 Spider Man 402 Transformers – Revenge of the Fallen 402 Star Wars Episode III – Revenge of the Sith 380

Find the Mean, Mode, and Median • Find the Median is 432. 5 Top Ten Movies and Revenue (millions) - 2008 Titanic 600 The Dark Knight 533 Star Wars 460 Shrek 2 436 E. T. 434 Star Wars Episode I – Phantom Menace 431 Pirates – Dead Man’s Chest 423 Spider Man 402 Transformers – Revenge of the Fallen 402 Star Wars Episode III – Revenge of the Sith 380

We Do • #1: Find the mean, median, and mode for each set of data. • Cost of a bus ride: $3. 25, $2. 50, $4, $8, $2. 50 – Mean: • 20. 20/5=$4. 05 – Median: • $3. 25 – Mode: • $2. 50

You Do • #2: Find the mean, median, and mode for each set of data. • Miles hikes the following distances (miles): • 5, 10, 9, 12, 8, 4, 5, 7, 5, 13, 11 – Mean: – Median: – Mode: 89/11 = 8. 1 mi 4, 5, 5, 5, 7, 8, 9, 10, 11, 12, 13 8 mi 5 mi

Understanding Average “Average” can be misleading. For example, take six workers in a company called Sunshine Desserts: Managing director = $100, 000 Marketing director = $45, 000 Secretary #1 = $15, 000 Secretary #2 = $15, 000 Accounts clerk = $15, 000 Receptionist = $10, 000 The average (mean) of these salaries is $33, 333, but that doesn’t give you a real idea of what the “average worker” earns in that particular company.

Think, Write, Share Managing director = $100, 000 Marketing director = $45, 000 Secretary #1 = $15, 000 Secretary #2 = $15, 000 Accounts clerk = $15, 000 Receptionist = $10, 000 What do you think is causing the average to reflect a higher income than the income of most of the workers? Why? �The Managing Director’s salary of $100, 000. This is more than double of any of the other salaries. We call this an “outlier” If we want to know what the “average” worker is making at this company, which central tendency would be better? Why? �The median because it does not include any outliers.

• Outlier: A data point that is distinctly separate from the rest of the data. • Ex. • 2, 4, 5, 7, 3, 5, 40, 6 • 40 is an outlier.

Understanding Outliers • The quiz scores for a math class are 8, 7, 6, 10, 0 and 8. • Mean w/ outlier 8 7 6 10 0 +8 39 39÷ 6= 6. 5 Mean w/out outlier 8 7 6 10 +8 39 39÷ 5= 7. 8

Understanding Outliers Which measure of central tendency was least affected by the outlier? A) Mean B) Median Which measure of central tendency should you use when there is an outlier? A) Mean B) Median

Measures of Central Tendency - Review • Mean – Average • Add up the values, divided by the number of values Skipare a line • Use when there no outliers • Median – Middle number in a list from least to greatest • When there are two, find the average Skipisa an lineoutlier • Use when there • Mode – Most popular or most frequently occurring number Skipvalues a line are non-numeric • Only use when the

Whiteboard Practice • Weights of babies(lbs) at birth were 7. 9, 7. 4, 8, 8. 4, 3. 4, 7 – What is the Mean – What is the Median – What is the Mode 7. 02 lbs 7. 65 lbs No Mode – Which Measure of Central Tendency is most appropriate? The Median – Why? We have an outlier

Whiteboard Practice �Utility bill for the past 6 months $129, $120, $140, $135, $112, $126 $127 ◦ What is the Mean ◦ What is the Median $127. 5 ◦ What is the Mode No Mode ◦ Which Measure of Central Tendency is most The Mean appropriate? No Outlier ◦ Why? ◦ Which would you use to convince the utility company Median that prices are too high?

Whiteboard Practice �Average market rent for a one bedroom apartment in Colorado Springs over the last six months: $550, $575, $580, $430, $525, $550 ◦ What is the Mean ◦ What is the Median ◦ What is the Mode $535 $550 ◦ Which measure of central tendency would the renter’s association use to show that rent is too high? Median/mode

White Board Practice UCCS CO College CU – Boulder Colorado State CU – Pueblo CU-Denver PPCC Mean: 19, 928. 6 Mode: none 21, 000 32, 500 19, 750 18, 250 20, 500 8, 000 Median: 19, 750 Texas A & M U. of Texas State TU - Dallas TU - Houston TCU CC of Austin 21, 500 30, 500 22, 500 19, 750 19, 000 18, 750 10, 000 Mean: 20, 285. 7 Mode: none Median: 19. 750 The tables show the tuition costs for colleges in two different states. Both Colorado and Texas claim to have the best tuition in the country. First: what do they mean by best? Lowest Second: Which measure of central tendency allows them both to be correct? Median - 19, 750

Essential Question • How do various measures of central tendency lead to different interpretations of the data?

DOL #1 • Your test scores this quarter: 65%, 95%, 83%, 75% • Which measure of central tendency should you ask your teacher to use in order to ensure you get the best grade? Explain why this is the case. a) Mean b)Median c) Mode d)Range

DOL #1 • Your test scores this quarter: 65%, 95%, 83%, 75% a) Mode None b) Median 158/2 = 79% 318/4=70. 5% c) Mean 2. Which measure of central tendency is the best and explain why? Mean: the mean offers you the chance to earn the highest possible grade.

D. O. L. #2 - Analyze Data • Compare and contrast the central tendencies of the salaries for the two stores. Based on the measures of central tendency, which store would you prefer to work? Justify you answer using mathematical reasoning. Hourly Salaries ($) Sports Extreme Superstore Sports 7, 24, 7, 6, 8, 9, 10, 8, 8, 8, 6 9, 8, 10

D. O. L. #2 - Analyze Data Hourly Salaries Sports Extreme Superstore Sports 7, 24, 7, 6, 8, 9, 10, 8, 8, 8, 6 9, 8, 10 • Mean = 9. 25 • Median = 7. 5 • Mode = 8 Mean = 9. 25 Median = 9. 5 Mode = 10 Justification for employment will vary.

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