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

Transcription

1 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

2 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

3 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

4 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

5 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 20 item data set. 63, 64, 65, 70, 74, 75, 80, 80, 83, 84, 85, 87, 88, 89, 90, 91, 97, 98, 99, 100 Percentile rank of 70: How many data points are less than or equal to 70? Put this number over the total number of data points and change to a percent. Percentile rank of 80 How many data points are less than or equal to 80? Put this number over the total number of data points and change to a percent. Percentile rank of 90: How many data points are less than or equal to 90? Put this number over the number of data points and change to a percent. 5

6 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

7 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

8 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 Draw a box with the vertical ends passing through the lower and upper quartiles. Draw a vertical line in box through the median. Connect the two extreme values to the box with lines called whiskers. 8

9 Example 1: Data: 2, 2, 5, 5, 5, 6, 8, 5, 8, 9, 10, 12, 7, 8, Arrange the data in order: 2. Draw number line to include 2 to 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

10 Example 2: Make a box and whisker plot from the following data Low score High score Median Lower quartile Upper quartile 10

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