Chapter 3.5 Five number summary
Symmetric box plot
Median is in the center of the box Left and right whiskers are roughly the same length
Skewed right box plot
Median is left of center in the box Left whisker is shorter than right whisker
Skewed left box plot
Median is right of center in the box Left whisker is longer than right whisker
Which measures are used in the five-number summary?
Min, Q1, Median, Q3, Max
For a distribution that is skewed left, the left whisker is _______ the right whisker.
longer than
Drawing a Boxplot
(1) Determine the lower and upper fences: Lower Fence= Q1−1.5(IQR) Upper Fence=Q3+1.5(IQR) where IQR=Q3−Q1 (2) Draw a number line long enough to include the maximum and minimum values. Insert vertical lines at Q1,M, and Q3. Enclose these vertical lines in a box. (3) Label the lower and upper fences with a temporary mark. (4) Draw a line from Q1 to the smallest data value that is larger than the lower fence. Draw a line from Q3 to the largest data value that is smaller than the upper fence. These lines are called whiskers. (5) Plot any data values less than the lower fence or greater than the upper fence as outliers. Outliers are marked with an asterisk (*). Remove the temporary marks labeling the fences.
The data to the right represent the number of chocolate chips per cookie in a random sample of a name brand and a store brand. Complete parts (a) to (c) below. Name Brand: 29 25 23 30 22 20 20 21 2633 27 22 25 Store Brand: 30 22 20 26 27 22 17 23 27 33 24 16 28 (b) Does there appear to be a difference in the number of chips per cookie? (c) Does one brand have a more consistent number of chips per cookie?
(b) Yes. The name brand appears to have more chips per cookie. (c) Yes. The name brand has a more consistent number of chips per cookie.
The following data represent the dividend yields (in percent) of a random sample of 28 publicly traded stocks. Compute the five-number summary for the data. 0.35 0.34 2.6 2.91 0.42 2.99 0.98 2.21 0.41 2.68 0 0.693.24 0.43 0.45 3.57 0 0.92 0.7 2.92 0 0.15 0 1.47 1.44 1.06 0.11 1.45
The five-number summary is 0, 0.345, 0.81, 2.405, 3.57
For a distribution that is skewed right, the median is________ of the box.
left of center
For a distribution that is symmetric, the left whisker is ________ the right whisker.
the same length as
five number summary
The five-number summary of a set of data consists of the smallest data value, Q1, the median, Q3, and the largest data value. We use the five-number summary to learn information about the extremes of the data set. The summary is organized as follows: