13Astem-leaf-plots

= Stem and Leaf Plots =


 * A ** Stem and Leaf Plot ** is a way of putting a moderately small amount of data into a table
 * There are two columns
 * The stem (all the digits except the units digit -- usually the tens digit)
 * The leaf (a list of each units digit from the values with that stem)
 * Each row shows the values with one stem
 * Most stem and leaf plots have a class interval of 10 so each stem appears once
 * If a class interval of 5 is used, each stem appears twice (as 3 and 3* for example) (see example 2)


 * If the plot is drawn neatly, it looks a bit like a histogram made up of numbers
 * It allows us to easily see the frequency of each class
 * the original data is not lost (unlike in an actual graph)


 * Example 1 **

Show in a stem and leaf plot: 23, 25, 30, 31, 31, 33, 35, 39, 42, 42, 47 48, 54


 * Solution:**

Note:
 * This stem and leaf plot shows a class interval of 10
 * the first row shows all values between 10 and 29
 * the second row shows all values between 30 and 39
 * etc
 * The key is important as it tells us how to understand the entries in the plot


 * Class Interval of 5 **

If the data is not very spread out, it may occupy only 2 or 3 rows of a Stem and Leaf plot like the one above. In this case, we can divide each row into two
 * the first row with leaves between 0 and 4
 * the second row with leaves between 5 and 9


 * Example 2 **

The heights of a group of students were collected.

... ... 174, 169, 168, 155, 171, 158, 165, 174, 173, 182 ... ... 175, 160, 174, 174, 178, 150, 160, 180, 161, 184

Display them in a Stem & Leaf Plot with a class interval of 5


 * Solution:**




 * Back to Back Stem & Leaf Plots **


 * Provides a simple but powerful way to visually compare two sets of data


 * The stem is in a column down the centre
 * The two sets of leaves are shown each side of the stem
 * The leaves are ordered with the smallest value closest to the stem


 * Example 3 **

The weights of a class of students were recorded in a back-to-back stem and leaf plot.

Compare the two sets of data


 * Solution:**


 * The boys are generally heavier than the girls


 * the most common weights (modal group) for the boys is 60-69 kg
 * the most common weights (modal group) for the girls is 40-49 kg


 * the median weight for boys (the 7th boy) is 60 kg
 * the median weight for girls (the 6.5th girl) is 48 kg


 * The boys and girls have a similar spread of values
 * the range of the boys is 78 – 43 = 35 kg
 * the range of the girls is 69 – 34 = 35 kg

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