BOX AND WHISKERS Section 11 2 pages 594

BOX AND WHISKERS Section 11. 2 pages 594 - 598

HOW TO MAKE A BOX AND WHISKERS • Place all values in numerical order from least to greatest. • Start with a number line (evenly spaced) that includes to smallest (called the Lower Extreme) and largest (called Upper Extreme) data values. • Find the median of the data. • Find the median of the lower half of the data called the Lower Quartile • Find the median of the upper half of the data called the Upper Quartile • Graph on the number line each data point calculated above. • Draw a box from LQ to Median and from Median to UQ • Draw a whisker (line) from LE to LQ and from UQ to UE Data in order: 18, 22, 24, 25, 25, 27, 28, 30, 30

TERMINOLOGY AND PURPOSE • A box-and-whisker plot shows the variability of a data set along a number line using the least value, the greatest value, and the quartiles of the data. • Quartiles divide the data set into four equal parts. • Range = Upper Extreme – Lower Extreme • Interquartile Range = Upper Quartile – Lower Quartile • The five numbers that make up a box-and-whisker plot are called the five-number summary of the data set. That is Lower Extreme, Lower Quartile, Median, Upper Quartile, and Upper Extreme. • Each Whisker represents 25% of the data • The Box represents 50% of the data • Looking at the box-and-whisker plot will help us determine if the data is evenly distributed, or if it is skewed (means the data is clustered in one quarter of the data more than in the other quarters).

The box-and-whisker plot represents the time (in hours) spent on a project by student in a history class. • Find and interpret the range of the data: • LE = 1, UE = 9. Range = 9 -1 = 8 hours • This means that the time spent on the project varies by no more than 8 hours. • Describe the distribution of the data: • 25% of the students spent between 1 and 3 hours on the project. • 50% of the students spent between 3 and 8 hours on the project. • 25% of the students spent between 8 and 9 hours on the project. • Find and interpret the interquartile range of the data: • The interquartile range is 8 – 3 = 5 hours. • This means that the middle half of the time spent on the project varies by no more than 5 hours. • Are the data more spread out below Q 1 (Lower Quartile) or above Q 3 (Upper Quartile)? Explain. • The data below Q 1 are more spread out than the data above Q 3. The lefr whiser is longer than the right whisker.

TRY IT: a) Identify the shape of each distribution: For your class, the left whisker is longer than the right whisker, and most of the data are on the right side of the plot. For your friend’s class, the whisker lengths are equal, and the median is in the middle of the plot. COMPARE AND EXPLAIN b) Which test scores are more spread out? Explain. The range and interquartile range of the test scores in your friend’s class are greater than the range and interquartile range in your class. So, the test scores in your friend’s class are more spread out. So, the distribution for your class is skewed left, and the distribution for your friend’s class is symmetric.

HOMEWORK: Do page 597 #3 -18 all