NAME: DIRECTIONS FOR THE ROUGH DRAFT OF THE BOX-AND WHISKER PLOT

Transcription

1 NAME: DIRECTIONS FOR THE ROUGH DRAFT OF THE BOX-AND WHISKER PLOT 1.) Put the numbers in numerical order from the least to the greatest on the line segments. 2.) Find the median. Since the data set has 36 numbers in it, the median will fall between two data points. In even numbered data sets, the median is not one of the data points. In odd numbered data sets, the median is one of the data points. Use a ruler and draw a line between the two numbers where the median is found. 3.) Since this is an even numbered data set, another calculation needs to be performed to obtain the median. The two numbers need to be averaged to find the middle number between them. Show the mathematical calculations for the median. For example, suppose the two numbers on either side of the median were 11.5 and Therefore, 11.8 is the median. Label this number as the median. Suppose the two numbers on either side of the median are 12.1 and It is evident the average between these two numbers to find the middle number is 12.1! Still show the mathematical calculations to prove the median is

2 4.) Count the numbers above the median and below the median. Make sure there is an equal amount of numbers on each side of the median. 5.) The lower quartile is also called Q1. To find the lower quartile, use the numbers less then the median. The word lower does not refer to the position of the numbers on the paper. The lower numbers in our case are positioned at the top of the page. To find the lower quartile, a.k.a. Q1, find the median of the numbers less than the median. 6.) Since the numbers less than the median is a data set with 18 numbers in it, the Lower Quartile or Q1 will fall between two data points. Use a ruler and draw a line between the two numbers where it falls. Suppose the two numbers on either side of the lower quartile are 8.2 and 8.2. It is evident the average between these two numbers to find the middle number is 8.2! Still show the mathematical calculations to prove the lower quartile is 8.2. Label the lower quartile Q1 or lower quartile ) The upper quartile is also called Q3. To find the upper quartile, use the numbers that are greater than the median. The word upper does not refer to the position of the numbers on the paper. The upper numbers in our case are positioned at the bottom of the page. To find the upper quartile, a.k.a. Q3, find the median of the numbers greater than the median. 8.) Repeat step 6 for the upper quartile, a.k.a. Q3. Label the upper quartile Q3 or upper quartile.

3 9.) Using a ruler, draw a box on the rough draft. One end of the box is the lower quartile (Q1) and the other end of the box is the upper quartile (Q3). The median will be drawn inside the box wherever it falls. Keep in mind, in the rough draft, the median will be exactly in the middle of the box. When the final draft of the box-and-whisker plot is made, the median falls anywhere inside the box. It may not be positioned in the middle of the box. Sometimes the median lies right on the box. These different scenarios are dependent upon the data. 10.) Using a ruler, draw one whisker from the lower quartile (Q1) to the minimum value of the data. Next, draw the other whisker from the upper quartile (Q3) to the maximum value of the data. 11.) How many parts to the box-and-whisker plot are evident? There should be 4 parts. Count to make sure an equal number of data points are in each section. Since each section represents 25% of the data, write 25% by each of the 4 sections. 12.) Along the left side of the rough draft, find the range of each of the 4 sections of the box-and-whisker plot. Show the mathematical calculations for each range. 13.) Write the five number summary in the lower right hand corner of the rough draft.

4 14.) Now you will determine if there are any outliers. STEP A STEP B STEP C STEP D STEP E STEP F OUTLIER CALCULATIONS Identify the Upper Quartile (Q3) and the Lower Quartile (Q1) Calculate the Interquartile Range (IQR): IQR = Q3 - Q1 Calculate: Q (IQR) Check the data for any values larger than the calculations from step C. If you find any, mark them as outliers (usually indicated on a graph by an asterisk). Calculate: Q1-1.5 (IQR) Check the data for any values smaller than the calculations from step E. If you find any, mark them as outliers (usually indicated on a graph by an asterisk). Outlier Calculations for Jump Data Step A: Q3 = Q1 = Step B: IQR = - = Step C: Step D: Q (IQR) = ( ) = List data larger then the calculated value: Are there any outliers? Explain why or why not. Step E: Step F: Q1-1.5 (IQR) = ( ) = List data smaller then the calculated value:

5 Are there any outliers? Explain why or why not. 15.) Now use the number line paper and make the final draft of the box-andwhisker plot.

6

7