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Bellwork 1. 2. 2 x 16 x 8 x 64 3 b 3 3b 2 2 4 b 12 Question Template • How many squares are there on a checkerboard? Recall that there are 8 squares on each side. • Hint: There are more than 64 squares. Definition Mean The mean of a numerical data set is the sum of the data divided by the number of data values. The symbol —x represents the mean. It is read as “x-bar.” Median The median of a numerical data set is the middle number when the values are written in numerical order. When a data set has an even number of values, the median is the mean of the two middle values. Mode The mode of a data set is the value or values that occur most often. There may be one mode, no mode, or more than one mode. Mean The average Median The number or average of the numbers in the middle Mode The number that occurs most These are Abby’s science test scores. 86 97 84 73 63 88 97 100 95 What can you tell us about these numbers? 86 73 97 97 63 100 84 88 95 What is the MEAN? How do we find it? The mean is the numerical average of the data set. The mean is found by adding all the values in the set, then dividing the sum by the number of values. 97 84 88 Lets find Abby’s MEAN science test score? 783 ÷ 9 The mean is 87 100 + 95 63 73 86 97 783 What is the MEDIAN? How do we find it? The MEDIAN is the number that is in the middle of a set of data 1. Arrange the numbers in the set in order from least to greatest. 2. Then find the number that is in the middle. 63 73 84 86 88 95 97 97 100 The median is 88. Half the numbers are Half the numbers are less than the median. greater than the median. Median Sounds like MEDIUM Think middle when you hear median. How do we find the MEDIAN when two numbers are in the middle? 1. Add the two numbers. 2. Then divide by 2. 63 73 84 88 95 97 97 100 88 + 95 = 183 183 ÷ 2 The median is 91.5 What is the MODE? How do we find it? The MODE is the piece of data that occurs most frequently in the data set. A set of data can have: One mode More than one mode No mode 63 73 84 86 88 95 97 97 100 The value 97 appears twice. All other numbers appear just once. 97 is the MODE A Hint for remembering the MODE… The first two letters give you a hint… Most Often MOde Which set of data has ONE MODE? A 9, 11, 16, 6, 7, 17, 18 B 18, 7, 10, 7, 18 C 9, 11, 16, 8, 16 Which set of data has NO MODE? A 9, 11, 16, 6, 7, 17, 18 B 18, 7, 10, 7, 18 C 13, 12, 12, 11, 12 Which set of data has MORE THAN ONE MODE? A B C 9, 11, 16, 8, 16 9, 11, 16, 6, 7, 17, 18 18, 7, 10, 7, 18 What is the RANGE? How do we find it? The RANGE is the difference between the lowest and highest values. 63 73 84 86 88 95 97 97 97 -63 34 34 is the RANGE or spread of this set of data What is the RANGE of this set of data? 99 48 97 84 86 71 88 What is the RANGE of this set of data? 48 71 88 97 99 86 84 99 -48 51 What is the RANGE of this set of data? 17 48 15 33 46 67 85 What is the RANGE of this set of data? 15 17 33 46 48 85 -15 70 67 85 Bellwork What is the MEAN, MEDIAN and RANGE of this set of data? 267 357 119 329 401 227 483 What is the RANGE of this set of data? 119 227 267 329 357 401 483 483 -119 364 This one is the requires more work than the others. Right in the MIDDLE. This one is the easiest to find— Just LOOK. https://www.youtube.com/watch?v=OvknM sRhGvg Find the…. Find the…. Find the…. Find the…. Find the…. Bellwork An amusement park hires students for the summer. The students’ hourly wages are shown in the table. a. Find the mean, median, and mode of the hourly wages. b. Which measure of center best represents the data? Explain. Outlier Find the standard deviation of the ages. Use a table to organize your work. Interpret your result. In Exercises 19–22, find (a) the range and (b) the standard deviation of the data set. 19. 20. 21. 22. 40, 35, 45, 55, 60 141, 116, 117, 135, 126, 121 0.5, 2.0, 2.5, 1.5, 1.0, 1.5 8.2, 10.1, 2.6, 4.8, 2.4, 5.6, 7.0, 3.3 Bellwork find (a) the range and (b) the standard deviation of the data set. 141, 116, 117, 135, 126, 121, 165,123. Outlier • An outlier is a data value that is much greater than or much less than the other values in a data set. • Should we include outliner in the data? Yes No No Effects of Data Transformations A data transformation is a procedure that uses a mathematical operation to change a data set into a different data set. Consider the data in Example. (a) Find the mean, median, mode, range, and standard deviation when each hourly wage increases by $0.50. (b) Find the mean, median, mode, range, and standard deviation when each hourly wage increases by 10%.