Comparing Statistical Data Mean Median Mode Range The average of a set of scores or data. The middle score or number when they are in ascending order. The score or number that appears most . The difference between the largest and the smallest score or number. Find the mean, median, and mode for the following distributions. Example 1 Example b 7, 4, 9, 3, 8, 0, 7, 4, 3, 7 4, 2, 5, 5, 1 1, 2, 4, 5, 5 Arrange the data in order 0, 3, 3, 4, 4, 7, 7, 7, 8, 9 The mean is the average 0, 3, 3, 4, 4, 7, 7, 7, 8, 9 1, 2, 4, 5, 5 = 4 The median is the middle value 1, 2, 4, 5, 5 = 5 The mode is the number that appears most 0, 3, 3, 4, 4, 7, 7, 7, 8, 9 = 7 The range is the difference between the largest & the smallest value 5 – 1 = 4 9 – 0 = 9

More Mean, Median, Mode & Range Find the mean, median, and mode for the following distributions. Example 1 Example b Example 3 3, 4, 5, 4, 3, 7, 2 1, 5, 2, 7, 3, 4, 6 2, 9, 3, 7, 3 1, 2, 3, 4, 5, 6, 7 2, 3, 3, 7, 9 2, 3, 3, 4, 4, 5, 7 Mean 1, 2, 3, 4, 5, 6, 7 2, 3, 3, 4, 4, 5, 7 Median 2, 3, 3, 7, 9 = 4 = 4 = 3 2, 3, 3, 4, 4, 5, 7 1, 2, 3, 4, 5, 6, 7 Mode 2, 3, 3, 7, 9 = 3 and 4 There is no mode = 3 Range 9 – 2 = 7 7 – 2 = 5 7 – 1 = 6

Using the Calculator to Analyze Data 4, 2, 5, 5, 1 17, 8, 20, 19, 26, 5, 9, 19, 6, 14, 12, 10, 13, 18 Enter values in L1 Store the data Press STAT ENTER (1-Var Stats) Press STAT > (CALC) ENTER Analyze the data That was easy

Finding Missing Values When the Mean is Known 105, 126, 110, 118, 113, x mean = 117 3.6, 4.8, 5.9, x mean = 5.1 Asi de Facil

Find mean, median, mode, & range Homework Page 742: 7- 10 Find mean, median, mode, & range Page 742: 11 – 14

Quartiles When data is listed in numerical order, the median separates it into two equal parts. The numbers that separate it into four equal parts are called quartiles. 53, 60, 61, 63, 64, 65, 65, 65, 65, 66, 66, 67, 67, 68, 69, 70, 70, 71, 71, 73 Lower Half Upper Half 53, 60, 61, 63, 64, 65, 65, 65, 65, 66, 66, 67, 67, 68, 69, 70, 70, 71, 71, 73 66 Median 53, 60, 61, 63, 64, 65, 65, 65, 65, 66, 66, 67, 67, 68, 69, 70, 70, 71, 71, 73 64.5 66 69.5 Median 1st Quartile 3rd Quartile 2nd Quartile

Using the Calculator to Find Quartiles 53, 60, 61, 63, 64, 65, 65, 65, 65, 66, 66, 67, 67, 68, 69, 70, 70, 71, 71, 73 Store the data Analyze the data Minimum Value = 53 1st Quartile = 64.5 Median = 66 3rd Quartile = 69.5 Maximum Value = 73

Box-and-Whisker Plot 53, 60, 61, 63, 64, 65, 65, 65, 65, 66, 66, 67, 67, 68, 69, 70, 70, 71, 71, 73 53, 60, 61, 63, 64, 65, 65, 65, 65, 66, 66, 67, 67, 68, 69, 70, 70, 71, 71, 73 64.5 66 69.5 53 73 Max Value Min Value 1st Quartile Median 3rd Quartile These five numbers are the statistical summary of the data. Draw a scale with numbers from the minimum value to the maximum value. Place dots above the scale to represent the five numbers that are the statistical summary of the data. Draw a box around the dots that represent the 1st & 3rd quartiles. Draw a vertical line through the dot representing the median. Connect the minimum value and the maximum value to the box with whiskers. 50 55 60 65 70 75

Another Box-and-Whisker Plot Let’s put the test score example into a Box-and-Whisker Plot. Student test scores: 90, 85, 74, 86, 65, 62, 100, 95, 77, 82, 50, 83, 77, 93, 73, 72, 98, 66, 45, 100, 50, 89, 78, 70, 75, 95, 80, 78, 83, 81, 72, 75 That was easy Asi de facil 40 50 60 70 80 90 100

For each Box-and-Whisker Plot, find the minimum value, the 1st quartile, the median, the 3rd quartile, and the maximum value. 30 40 50 60 70 80 90 MIN 40 Q1 58 MED 64 Q3 74 MAX 88 50 55 60 65 70 75 80 MIN 51 Q1 57.5 MED 60 Q3 65.5 MAX 78

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