Standard Deviation

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Standard Deviation. Understanding the Mean. 2009 3.17c. Taken from Virginia Department o f Education “Mean Balance Point”. Where is the balance point for this data set?. X. X. X. X. X. X. Taken from Virginia Department o f Education “Mean Balance Point”.
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Standard DeviationUnderstanding the Mean2009 3.17cTaken from Virginia Department o f Education “Mean Balance Point”Where is the balance point for this data set?XXXXXXTaken from Virginia Department o f Education “Mean Balance Point”Where is the balance point for this data set?XXXXXXTaken from Virginia Department o f Education “Mean Balance Point”Where is the balance point for this data set?XXXXXXTaken from Virginia Department o f Education “Mean Balance Point”Where is the balance point for this data set?XXXXXXTaken from Virginia Department o f Education “Mean Balance Point”Where is the balance point for this data set?3 is theBalance PointXXXXXXTaken from Virginia Department o f Education “Mean Balance Point”Where is the balance point for this data set?MEANSum of the distances below the mean1+1+1+2 = 5Sum of the distances above the mean2 + 3 = 5XXXXXXTaken from Virginia Department o f Education “Mean Balance Point”Where is the balance point for this data set?Move 2 StepsMove 2 StepsMove 2 StepsMove 2 Steps4 is the Balance PointTaken from Virginia Department o f Education “Mean Balance Point”9We can confirm this by calculating:2 + 2 + 2 + 3 + 3 + 4 + 5 + 7 + 8 = 3636 ÷ 9 = 4The Mean is the Balance Point 10Where is the balance point for this data set?If we could “zoom in” on the space between 10 and 11, we could continue this process to arrive at a decimal value for the balance point.Move 1 StepThe Balance Point is between 10 and 11 (closer to 10).Move 2 StepsMove 1 StepMove 2 StepsTaken from Virginia Department o f Education “Mean Balance Point”11Place the 8 sticky notes as a group so that exactly 3 are ‘16’, and one is ’12’. Place the remaining four numbers so that the balance point is 16. Then find the sum of deviations from the center.
• Place the 9 sticky notes as a group so that exactly 1 is ‘11’, two are ‘17’ and two are ’16’. None of the remaining ones have ’16’ Place the remaining four numbers so that the balance point is 16. Then find the sum of the deviations from the center.
• Taken from Virginia Department o f Education “Mean Balance Point”[Which of the following will have the most variability?
• [Heights of people in this room]
• [Ages of people in this room]
• [The number of countries that people have been to in this room?]
• [Default][MC Any][MC All]Variability: How close the numbers are together. Standard deviation: (Sx or )Way to measure the variability. Closer to zero is better!Sum of Distances from Center: -2,-2,-2,-1,-1,0,1,3,4 = 0 Sum of Squares of distances: 4,4,4,1,1,0,1,9,16=40 from center: Average (with one less member) of the squares of the distance from the center: VARIANCE 40/8=5Square root of the VARIANCE: 2.23 so the STANDARD DEVIATION (Sx) is 2.23Now find the STANDARD DEVIATION of your Poster15Taken from Core Plus MathematicsGrams of FatBig Mac: 31BK Whopper: 46Taco Bell Beef Taco: 10Subway Sub w/toppings: 44.5Dominoes Med. Cheese Pizza: 39KFC Fried Chicken: 19Wendy’s Hamburger: 20Arby’s Roast Beef Sandwich: 19Hardee’s Roast Beef Sandwich: 10Pizza Hut Medium Cheese Pizza: 39Calculator Method
• 1) Put the numbers into STAT EDIT
• 2) Do STAT CALC 1-VAR STATS.
• The is the “mean”
• The Sx is the standard deviation
• The is a standard deviation we will not use
• The n is the amount of data (good way of checking)
• The ‘med’ is the median (scroll down)
• Which would have a lower standard deviation? (Be prepared to explain):
• [The heights of students in this class]
• [The heights of students in this school]
• [Default][MC Any][MC All]Normal DistributionBell Curvehttp://en.wikipedia.org/wiki/File:Standard_deviation_diagram.svghttp://en.wikipedia.org/wiki/SkewnessDetermine if the following examples are Normally Distributed, Positively Skewed, or Negatively Skewed. Place the following under negatively skewed, normally distributed, or positively skewed, or random?
• The amount of chips in a bag
• The sum of the digits of random 4-digit numbers?
• The number of D1’s that students in this class have gotten?
• The weekly allowance of students
• Age of people on a cruise this week
• F) The shoe sizes of females in this classWhich is more likely to make a better bell curve, measuring the heights of people in this room or measuring the heights of people in this school? http://www.shodor.org/interactivate/activities/NormalDistribution/SAT Scores 5000200 300 400500600 700 800The SAT’s are Normally Distributed with a mean of 500 and a standard deviation of 100.A) Give a Title and fill in the bottom row B) What percentage of students score above a 600 on the SAT? C) What percentage of students score between 300 and 500?D) If Jane got a 700 on the SAT, what percentile would she be?E) Mt. Tabor has 1600 students, how many students are expected to get at least a 700? 15.847.7100-2.2 97.8.022*1600 = 35 studentsIQ’s of Humans 5000 50 66.7 83.3100116.7 133.3 150The IQ’s are Normally Distributed with a mean of 100 and a standard deviation of 16.667.2.2A) What percentage of people have an IQ below 66.7? B) A genius is someone with IQ of at least 150? What percentage?C) If Tom’s IQ is 83.3, what percentile would he be?D) Spring School has 1000 students, how many students are expected to have at least a 133.3 IQ? E) What number represents a Z-score of 1.5?.115.8.022 * 1000 = 22100+1.5(16.667) = 125The following is the amount of black M&M’s in a bag: 12, 13,14, 15, 15, 16, 17, 20, 21,22,23,24,25 Find the mean and standard deviation
• [18.23, 4.46]
• [18.23, 4.28]
• [Default][MC Any][MC All]The following is the amount of black M&M’s in a bag: 12, 13,14, 15, 15, 16, 17, 20, 21,22,23,24,25 What percentage is above 22.6 black M&M’s?
• 15.8
• 0.3
• Memory GameDog, cat, monkey, pig, turtle, apple, melon, banana, orange, grape, desk, window, gradebook, pen, graph paper,Stove, oven, pan, sink, spatula,Shoes, tie, bracelet, necklace, boot
• Find the mean and standard deviation with your calculator
• Is it positively skewed, negatively skewed, or normally skewed?
• The more people with same data means lower standard deviation.
• A lower standard deviation means less variability.
• Z score is how many standard deviations you are from the mean. The higher of the absolute value of the z-score indicates the less likelihood of the event happening.
• Ex: Z score of 2 is more remarkable than a z score of 1 Ex 2: A mean of 7, stdeviation of 3. A z-score of -1.5 would be 7+(-1.5)*3 = 2.5Debate:
• Side 1) You are trying to convince your teacher to always curve test grades to a standard deviation
• Side 2) You are trying to convince your teacher to never curve test grades to a standard deviation
• Summarize the MathematicsA) Describe in words how to find the standard deviation.B) What happens to the standard deviation as you increase the sample size?C) Which measures of variation (range, interquartile range, standard deviation) are resistant to outliers. ExplainD) If a deviation of a data point from the mean is positive, what do you know about its value? What if the deviation is zero?E) What do you know about the sum of all the deviations of the mean?F) Suppose you have two sets of data with an equal sample size and mean. The first data set has a larger deviation than the second one. What can you conclude?Adult female dalmatians weigh an average of 50 pounds with a standard deviation of 3.3 pounds. Adult female boxers weigh an average of 57.5 pounds with a standard deviation of 1.7 pounds. The dalmatian weighs 45 pounds and the boxer weighs 52 pounds. Which dog is more underweight? Explain….http://www.rossmanchance.com/applets/NormalCalcs/NormalCalculations.htmlOne way to measure light bulbs is to measure the life span. A soft white bulb has a mean life of 700 hours and a standard deviation of 35 hours. A standard light bulb has a mean life of 675 hours and a standard deviation of 50 hours. In an experiment, both light bulbs lasted 750 hours. Which light bulb’s span was better?http://www.rossmanchance.com/applets/NormalCalcs/NormalCalculations.htmlThink back to the two overweight people shown on the first slide. How could we now determine which one is more overweight?
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