BOXANDWHISKER PLOT Adapted by J Delilovic BOXANDWHISKER PLOT

BOX-AND-WHISKER PLOT Adapted by J. Delilovic

BOX-AND-WHISKER PLOT A box-and-whisker plot is a method of representing data. It looks like this. 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 Whisker BOX

In a box-and-whisker plot, each section from dot to dot (each quartile) represents ¼ or 25% of the data. The total represented by the entire plot is 100%. 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 25% 50%

Drawing a Box-and-Whisker Plot To draw a box-and-whisker plot, we must first find 5 number summaries: l l l Least Value - Minimum (median of lower half) Lower Quartile Median (median of upper half) Upper Quartile Greatest Value - Maximum

Let’s Make a Box-and-Whisker Plot in Our Notes Draw a box-and-whisker plot for this data: 4, 7, 15, 27, 9, 14, 12, 22, 9, 11, 18 First, we must put these numbers in order from least to greatest.

Order the Data 4, 7, 9, 9, 11, 12, 14, 15, 18, 22, 27 Now we can find the 5 number summary. Let’s list them

Least and Greatest Value 4, 7, 9, 9, 11, 12, 14, 15, 18, 22, 27 1. Least Value 4 2. Lower Quartile Least and greatest values are the smallest and the largest data. 3. Median 4. Upper Quartile 5. Greatest Value 27

Median Find the median of the entire group of data. What number is in the middle? 13 4, 7, 9, 9, 11, 12, 14, 15, 18, 22, 27 12 + 14 2

4, 7, 9, 9, 11, 12, 14, 15, 18, 22, 27 1. Least Value 4 2. Lower Quartile 3. Median 13 4. Upper Quartile 5. Greatest Value 27

Lower Quartile Lower quartile is the median of the lower half of data. What number is in the middle? 9 13 4, 7, 9, 9, 11, 12, 14 15, 18, 22, 27 Lower half 9+9 2

Draw a box-and-whisker plot for this data: 4, 7, 9, 9, 11, 12, 14, 15, 18, 22, 27 1. Least Value 2. Lower Quartile 3. Median 4 9 13 4. Upper Quartile 5. Greatest Value 27

Upper Quartile Upper quartile is the median of the second half of data. What number is in the middle? 13 16. 5 4, 7, 9, 9, 11, 12, 14, 15, 18, 22, 27 Second half 15 + 18 2

4, 7, 9, 9, 11, 12, 14, 15, 18, 22, 27 1. Least Value 2. 3. 4. 5. 4 Lower Quartile 9 Now we can draw Median 13 a box and whisker plot Upper Quartile 16. 5 Greatest Value 27

Draw a number line that is large enough to include the smallest and the largest data value. 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

Put the dot for all five values. Draw the lines through the median and both quartiles. Lower Extreme Lower Quartile Median Upper Quartile Upper Extreme 4 9 13 16. 5 27 Connect them with two horizontal lines to create a box. 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 Finally, connect lower quartile and the least value with a whisker. Do the same with upper quartile and the greatest value.

Interquartile Range The difference between the upper and the lower quartiles. Tells us between which two values is 50% of the data. 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 So, 50% of the data is between 16. 5 and 9

While 50% of the data is between 16. 5 and 9, 25% is between 4 and 9 and 25% is between 16. 5 and 27. 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30