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Sec. 3.2

Sec. 3.2. Displaying Numerical Data: Stem-and-Leaf Displays. Stem-and-Leaf Diagram. A quick technique for picturing the distributional pattern associated with numerical data is to create a picture called a stem-and-leaf diagram (Commonly called a stem plot).

jebediah-harrison
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Sec. 3.2

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  1. Sec. 3.2 Displaying Numerical Data: Stem-and-Leaf Displays

  2. Stem-and-Leaf Diagram A quick technique for picturing the distributional pattern associated with numerical data is to create a picture called a stem-and-leaf diagram (Commonly called a stem plot). • We want to break up the data into a reasonable number of groups. • Looking at the range of the data, we choose the stems (one or more of the leading digits) to get the desired number of groups. • The next digits (or digit) after the stem become(s) the leaf. • Typically, we truncate (leave off) the remaining digits.

  3. When to Use Stem-and-Leaf Displays Numerical data sets with a small to moderate number of observations. This does NOT work well with very large data sets.

  4. How to Construct a Stem-and-Leaf Display • Select one or more leading digits for the stem values. The trailing digits (or sometimes just the first one of the trailing digits) become the leaves. • List possible stem values in a vertical column. • Record the leaf for every observation beside the corresponding stem value. • Indicate the units for stems and leaves somewhere in the display.

  5. What a Stem-and-Leaf Display Shows • A representative or typical value in the data set. • The extent of the spread about such a value. • The presence of any gaps in the data. • The extent of the symmetry in the distribution of values. • The number and location of peaks. • The presence of any outliers.

  6. 10 11 12 13 14 15 16 17 18 19 20 3 3 154504 90050 000 05700 0 0 5 0 Stem Plot For our first example, we use the weights of 25 female students. Choosing the 1st two digits as the stem and the 3rd digit as the leaf we have the following: 150 140 155 195 139 200 157 130 113 130 121 140 140 150 125 135 124 130 150 125 120 103 170 124 160

  7. 10 11 12 13 14 15 16 17 18 19 20 3 3 014455 00059 000 00057 0 0 5 0 Stem Plot Typically we sort the order of the stems in increasing order. We also note on the diagram the units for stems and leaves Probable outliers Stem: Tens and hundreds digits Leaf: Ones digit

  8. Definition: Outlier An outlier is an unusually small or large data value.

  9. When to Use Stem-and-Leaf Displays Use with numerical data sets with a small to moderate number of observations. NOTE: Stem-and-leaf displays do not work well with very large data sets.

  10. Stem-and-leaf: GPA example The following are the GPAs for the 20 advisees of a faculty member. GPA 3.09 2.04 2.27 3.94 3.70 2.69 3.72 3.23 3.13 3.50 2.26 3.15 2.80 1.75 3.89 3.38 2.74 1.65 2.22 2.66 If the ones digit is used as the stem, you only get three groups. You can expand this a little by breaking up the stems by using each stem twice letting the 2nddigits 0-4 go with the first and the 2nd digits 5-9 with the second. The next slide gives two versions of the stem-and-leaf diagram.

  11. 1L 1H 2L 2H 3L 3H 65,75 04,22,26,27 66,69,74,80 09,13,15,23,38 50,70,72,89,94 1L 1H 2L 2H 3L 3H 67 0222 6678 01123 57789 Stem-and-leaf: GPA example Stem: Ones digit Leaf: Tenths digits Stem: Ones digit Leaf: Tenths and hundredths digits Note: The characters in a stem-and-leaf diagram must all have the same width, so if typing, use a fixed-character width font such as COURIER.

  12. 3 10 3 11 7 554410 12 145 95000 13 0004558 000 14 000000555 75000 15 0005556 0 16 00005558 0 17 000005555 18 0358 5 19 0 20 0 21 0 22 55 23 79 Comparative Stem and Leaf DiagramStudent Weight (Comparing two groups) female male When it is desirable to compare two groups, back-to-back stem and leaf diagrams are useful. Here is the result from the student weights. From this comparative stem and leaf diagram, it is clear that the males weigh more (as a group, not necessarily as individuals) than the females.

  13. female male 7 1 9999 1 888889999999999999999 1111000 2 00000001111111111 3322222 2 2222223333 4 2 445 2 6 2 88 0 3 3 3 7 3 8 3 4 4 4 4 7 4 Comparative Stem and Leaf DiagramStudent Age From this comparative stem and leaf diagram, it is clear that the male ages are all more closely grouped then the female ages. Also, the females have a number of outliers.

  14. Assignment • WS Graphing • Due on Monday, 08 September 2014. • Sec. 3.2: pp. 96-97 (3.17 – 3.22 all) • Due on Monday, 08 September 2014.

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