Math I - Notes Box and Whisker Plots I CAN create a box and whisker plot I CAN interpret a box and whisker plot A box and whisker plot is a data display that organizes data values into _4_ groups.

INTERPRETING Box and Whisker Plots - A box and whisker plot separates data into FOUR sections…The two parts of the box and two whiskers. All four sections contain about the same number of data values. **The lengths of the sections tell you how spread out the data are.**

The large box represents About half of the data Lower Quartile Upper Quartile 264 370 452 459 572 Each whisker Each whisker represents about represents about 25% of the data Median 25% of the data

Lower Quartile - The _Median_ of the lower half Definitions: Lower Quartile - The _Median_ of the lower half Upper Quartile - The MEDIAN of the _Upper_ half Lower Extreme - The __smallest__ data value Upper Extreme - The greatest ___data___ value

1. Order your data from least to greatest Steps for creating a box and whisker plot: 1. Order your data from least to greatest 2. Find the median of your data 3. Find the quartiles of your data (the median of the upper and lower half) **When a data set has an odd number of values, do NOT include the median in either half of the data when determining the quartiles. ** 4. Find the extremes of your data (the least and greatest values) 5. Plot the median, quartiles, and extremes below a number line (USE A RULER TO MAKE SURE YOUR NUMBER LINE “TICK MARKS” ARE EVENLY SPACED!!) 6. Draw the box and the whiskers

Example: Create a box and whisker plot using this data: 7, 19, 6, 12, 5, 17, 6, 13 1 “order” 5 6 6 7 12 13 17 19 2 Find the Median = 7+12= 19 /2 = 9.5 3 5 6 6 7 9.5 12 13 17 19 Lower quartile=__6__ Upper quartile= ____15_____ 4 Lower extreme = ___5____ Upper extreme = ____19____ 5 6 9.5 15 19

Create a box and whisker plot using this data: 14, 6, 13, 17, 1, 12, 9, 18. Show all 4 steps and work neatly below. Order… 1, 6, 9, 12, 13, 14, 17, 18 Median… 12.5 Lower Quartile= 7.5 Upper Quartile = 15.5 Lower Extreme = 1 Upper Extreme = 18 1 7.5 12.5 15.5 18

Create a box and whisker plot using this data: 77, 99, 112, 85, 117, 68, 63. Show all 4 steps and work neatly below. Order… 63, 68, 77, 85, 99, 112, 117 Median… 85 Lower Quartile = 68 Upper Quartile = 112 Lower Extreme = 63 Upper Extreme = 117 63 68 85 112 117

The box-and-whisker plots below show a class’ test scores for two tests. What conclusions can you make? The ____UPPER EXTREMES___ are the same for both tests. The median for the second test is ___LARGER___ than the median for the first test. The __UPPER QUARTILE__ for the first test is the same as the _MEDIAN__ for the second test. The scores for the _TEST 1_ are more spread out than the scores for the __TEST 2 __. Both range (91 – 62 = _29_) and the interquartile range (84 – 74 = _10_) of the first test are __LARGER__ than the range (91 – 71 = _20_) and the interquartile range (88 – 80 = _8_) of the second test. Inner quartile range is ______the difference between the upper quartile and the lower quartile___________