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Day 4 ­ Percentiles and Box and Whisker.Notebook April 20, 2018

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Day 4 ­ Percentiles and Box and Whisker.Notebook April 20, 2018 Day 4 ­ Percentiles and Box and Whisker.notebook April 20, 2018 Day 4 ­ Box & Whisker Plots and Percentiles In a previous lesson, we learned that the median divides a set a data into 2 equal parts. Sometimes it is necessary to divide the data into smaller more precise parts. We can divide data into 4 equal parts called quartiles. The following diagram illustrates how this works: 1 Day 4 ­ Percentiles and Box and Whisker.notebook April 20, 2018 Example: Find the median, first quartile and third quartile of the following data: {43, 42, 73, 74, 78, 82, 86, 80, 80, 87, 97, 91, 91} Step 1: Arrange in order­ lowest to highest. Step 2: Find and label the median. Step 3: Find and label the median of the lower half. Label this 1st Quartile. Step 4: Find the median of the upper half. Label this appropriately as the 3rd Quartile. 2 Day 4 ­ Percentiles and Box and Whisker.notebook April 20, 2018 The five number summary of a set of data includes the minimum, the 1st quartile, the median, the 3rd quartile and the maximum. The minimum is the least value and the maximum is the greatest value. Find the five number summary for the data below: 125 , 140, 80, 135, 126, 140, 350 The five number summary is min _____, 1st Q _____, median _____, 3rd Q ______, max _______ 3 Day 4 ­ Percentiles and Box and Whisker.notebook April 20, 2018 Percentiles are another way to divide data into even more precise groups. You have all seen percentiles when your guidance councilor talked to you about your performance on standardized tests. Percentiles separate data sets into 100 equal parts. The percentile rank of a score tells us the percent of values in the set less than or equal to that member. The median describes the _____th percentile. The first quartile describes the _____th percentile. The third quartile describes the _____th percentile. 4 Day 4 ­ Percentiles and Box and Whisker.notebook April 20, 2018 Example: Of 25 test scores, eight are less than or equal to 75. What is the percentile rank of a test score of 75? Write a ratio of the number of score less than or equal to 75 compared to the total number of test scores Find the percentile rank of the following using the 20­item data set. 63, 64, 65, 70, 74, 75, 80, 80, 83, 84, 85, 87, 88, 89, 90, 91, 97, 98, 99, 100 ꞏ Percentile rank of 70: How many data points are less than or equal to 70______? ꞏ Put this number over the total number of data points and change to a percent. ꞏ Percentile rank of 80 How many data points are less than or equal to 80______? ꞏ Put this number over the total number of data points and change to a percent. ꞏ Percentile rank of 90: How many data points are less than or equal to 90 ______? ꞏ Put this number over the number of data points and change to a percent. 5 Day 4 ­ Percentiles and Box and Whisker.notebook April 20, 2018 16 students received the following scores on a math quiz. 60, 62, 62, 65, 70, 74, 74, 76, 78, 82, 85, 94, 96, 98, 98, 99 Find the median __________ Find the first quartile __________ Find the third quartile _____________ What is the percentile rank of 94? In fraction form ______ in decimal form _____ in percent form ____ What is the percentile rank of 98? In fraction form ______ in decimal form _____ in percent form ____ What is the percentile rank of 74? In fraction form ______ in decimal form _____ in percent form ____ 6 Day 4 ­ Percentiles and Box and Whisker.notebook April 20, 2018 A Box and Whisker Plot is a graph that describes data using the five number summary of a set. This plot is useful for comparing two or more data sets. The Box and Whisker Plot shows how the data for each set are distributed and what the extreme values are. Terms: median: the middle piece of data (50%) first or lower quartile : middle of lower half of data (25%) third or upper quartile: middle of upper half of data (75%) interquartile range: difference between the third and first quartile DATA MUST BE PUT INTO NUMERICAL ORDER BEFORE A BOX AND WHISKER PLOT CAN BE CONSTRUCTED 7 Day 4 ­ Percentiles and Box and Whisker.notebook April 20, 2018 Steps in constructing a Box and Whisker Plot 1. Arrange the values in numerical order 2. Draw a number line to include the lowest and highest value in the data set 3. Calculate the median, the lower quartile and the upper quartile 4. Place dots above the number line to mark the 5 values : lowest value, lower quartile, median, upper quartile, and highest value ꞏ Draw a box with the vertical ends passing through the lower and upper quartiles. Draw a vertical line in box through the median. ꞏ Connect the two extreme values to the box with lines called whiskers. 8 Day 4 ­ Percentiles and Box and Whisker.notebook April 20, 2018 Example 1: Data: 2, 2, 5, 5, 5, 6, 8, 5, 8, 9, 10, 12, 7, 8, 11 1. Arrange the data in order: 2. Draw number line to include 2 to 12 3. Determine the median = lower quartile = upper quartile = 4. Mark points the 5 data points 5. Draw box and whiskers. 6. What is the interquartile range? 9 Day 4 ­ Percentiles and Box and Whisker.notebook April 20, 2018 Example 2: Make a box and whisker plot from the following data Low score ________ High score ________ Median ___________ Lower quartile __________ Upper quartile ___________ 10 Day 4 ­ Percentiles and Box and Whisker.notebook April 20, 2018 11 Day 4 ­ Percentiles and Box and Whisker.notebook April 20, 2018 12.
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