11 2 BOX AND WHISKER PLOTS WHAT WE

11. 2 BOX AND WHISKER PLOTS

WHAT WE WILL LEARN • Make and use box and whisker plots • Interpret box and whisker plots • Use to compare data sets

NEEDED VOCAB • Box and whisker plot: shows the variability of a data set along a number line using least, greatest, and quartiles. • Quartile: divide data set into four equal parts • Five number summary: least value, first quartile, median, third quartile, and greatest value that make up a box and whisker plot • Interquartile range: represents the middle half of the data

EX. 1 MAKING A BOX AND WHISKER PLOT • • • Steps 1. put numbers in numerical order 2. make a number line 3. put a dot at highest and lowest value 4. find median and put a dot 5. find Q 1 • Median of low to median • 6. find Q 3 • Median of high to median • Make a box and whisker plot of: • 24, 30, 22, 25, 22, 18, 25, 28, 30, 25, 27

YOUR PRACTICE • A basketball player scores 14, 16, 20, 5, 22, 30, 16, and 28 points during a tournament. Make a box and whisker plot that represents the data. • 5, 14, 16, 20, 22, 28, 30

EX. 2 INTERPRETING • Interquartile range (IQR) is third quartile (Q 3) – first quartile (Q 1) • Range of middle half of data

EX. 2 CONTINUED • The box and whisker plot represents the lengths (in seconds) of the songs played by a rock band at a concert. • A. find and interpret the range of data • Range is high minus low • To interpret: things vary by this amount • B. describe the distribution of the data • 25% in each whisker • 50% in the box • C. find and interpret the interquartile range • Q 3 - Q 1, middle half varies by this amount • D. is the data more spread out below Q 1 or above Q 3? • Look for longer whisker

EX. 2 CONTINUED • A. find and interpret range of the data • 300 – 160 = 140, so length of songs vary by 140 seconds • B. describe distribution • 25% between 160 and 220 seconds • 50% between 220 and 280 seconds • 25% between 280 and 300 seconds • C. find and interpret interquartile range • 280 – 220 = 60, so middle half of songs vary by 60 seconds • D. where is data more spread out • Below Q 1

EX. 3 COMPARING BOX AND WHISKER PLOTS

EX. 3 CONTINUED • A. identify the shape of each distribution • Your class – skewed left • Friend’s class - symmetric • B. which scores are more spread out? • Friend’s class