Box_and_Whiskers_Problem


 * Student Name:** Linda Fahlberg

**Statement of Problem: You catch and measure the length of ** 13 fish in a lake ** : 12, 13, 5, 8, 9, 20, 16, 14, 14, 6, 9, 12, 12 **
What do I need to do: Use the Rule of Four with a Box and Whiskers plot to completely describe this problem.
 * Questions: ** What is the median value of the data; what is the mean value of the data?
 * the first quarter of the data numbers are less than or equal to ** _ _ **
 * the second quarter of the data numbers are between ** _ _ ** and ** _ _ **
 * the ** _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ** of the data numbers are between 12 and 14
 * the last quarter of the data numbers are ** _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ** 14

Rule 1: Description of problem. To find a box and whisker plot, we must first sort the data: 5, 6, 8, 9, 9, 12, 12, 12, 13, 14, 14, 16, 20. Then we find the median and the first and third quartiles. There are 6 data numbers. This is an even number so we find the mean of these middle data numbers. That is: Q1=(8+9)/2=**8.5** There are 6 data numbers. This is an even number so we find the mean of these middle data numbers. That is: Q1=(14+14)/2=**14**
 * Median:** There are 13 data numbers. This is an odd number, so the middle data number is the median. (13-1)/2 + 1=7. The 7th data number is **12**.
 * First quartile:** We find the median of all the data numbers to the left of the 7th data number: 5, 6, 8, 9, 9,12.
 * Third quartile:** We find the median of all the data numbers to the right of the 7th data number: 12, 13, 14, 14, 16, 20

Rules 2-4: **GeoGebra worksheet with Algebra - Graph - Table** media type="custom" key="6499779"

** Questions: ** What is the median value of the data; what is the mean value of the data?
 * Answers:** The ** median of the data is 12. ** The mean of the data is the average so: 5 + 6 + 8 + 9 + 9 + 12 + 12 + 12 + 13 + 14 + 14 + 16 + 20)/13 = ** 11.54 **
 * the first quarter of the data numbers are less than or equal to ** _8.5_ **
 * the second quarter of the data numbers are between ** _8.5_ ** and ** _12_ **
 * the ** _third quarter_ ** of the data numbers are between 12 and 14
 * the last quarter of the data numbers are ** _greater than or equal to_ ** 14

Remember - If the original **sorted** data set has an **even** number of data numbers, then the
 * **first quartile** is the median of the **entire first half** of the data set and the
 * **third quartile** is the median of the **entire second half** of the data set.