1. Box and Whisker Plots and Quartiles Sixth Grade

2. Five Statistical Summary When describing a set of data we have seen that we can use measures such as mean and median. We can also get a sense of the data’s distribution by examining a five statistical summary. (1) minimum, (2) maximum, (3) median (second quartile), (4) first quartile, and (5) third quartile.

3. Quartiles We know that the median of a set of data separates the data into two equal parts. Data can be further separated into quartiles. Quartiles separate the original set of data into 4 equal parts. Each of these parts contains one-fourth of the data. Quartiles are percentiles that divide the data into fourths.

4. First Quartile The first quartile is the middle (the median) of the lower half of the data. One-fourth of the data lies below the first quartile and three-fourths lies above. The 25 th percentile.

5. Second Quartile The second quartile is another name for the median of the entire set of data. Median of data set = second quartile of data set The 50 th percentile.

6. Third Quartile The third quartile is the middle (the median) of the upper half of the data. Three-fourths of the data lies below the third quartile and one-fourth lies above. The 75 th percentile. A QUARTILE IS A NUMBER, IT IS NOT A RANGE OF VALUES. A VALUE CAN BE DESCRIBED AS ‘ABOVE’ OR ‘BELOW’ THE FIRST QUARTILE, BUT A VALUE IS NEVER ‘IN’ THE QUARTILE.

7. Consider the following… Minimum 65 First quartile 70 Second quartile (Median) 80 Third quartile 90 Maximum 100 While we do not know every test score, we do know that half of the scores are below 80 and half are above 80. We also know that half of the scores are between 70 and 90. The difference between the third and first quartiles is called the inter-quartile range. IQR = 20.

8. Find the first, second and third quartiles. 1) 4, 3, 6, 5, 2 2) 12, 10, 8, 14, 18, 6 3) 10, 15, 12, 16, 20 4) 5, 2, 3, 8, 7, 12 5) 7, 13, 9, 18, 20, 12

9. Answers QuestionFirst QuartileSecond QuartileThird Quartile 12.545.5 281114 3111518 4368 591318

10. More Practice 1) 4, 6, 5, 6, 2, 7, 6, 8 2) 17, 14, 20, 29, 12, 24, 10, 19 3) 68, 88, 44, 68, 50, 68, 37, 50 4) 52, 60, 24, 36, 48, 52, 72 5) 102, 78, 312, 170, 250, 40, 52, 38, 125

11. Answers QuestionFirst QuartileSecond QuartileThird Quartile 14.566.5 2131822 3475968 4365260 546102210

12. Box-and-Whisker Plot A five statistical summary can be represented graphically as a box-and-whisker plot. The first and third quartiles are at the end of the box plot, the median is indicated with a vertical line in the interior of the box, and the maximum and minimum are at the ends of the whiskers. http://www.khanacademy.org/math/probability/descr iptive-statistics/Box-and- whisker%20plots/e/creating_box_and_whisker_plots