STEM-AND-LEAF DISPLAYS

1
STEM-AND-LEAF DISPLAYS
Uses actual data values to create a graph

• STEPS
• 1. Select a typical data value.
• 2. Divide this number into leading and trailing
  digits.
• 3. Write down all possible sets of leading digits
  in order from the lowest to highest as a column.
  These are stems.
• 4. For each data value write down the first
  trailing digit on the line labeled by its leading
  digits. These are the leaves. One leaf for each
  data value.

2
STEM-AND-LEAF DISPLAYS

• Uses actual data values to create a graph (pulse
  rates of 39 Peruvian Indians)
• 52, 56, 60, 60, 60, 60, 60, 60, 64, 64, 64, 64,
  64, 64, 64, 68, 68, 68, 68, 72,
• 72, 72, 72, 72, 72, 72, 72, 74, 76, 76, 76, 76,
  80, 80, 84, 88, 88, 88, 92

• STEPS
• 1. Select a typical data value.
• 2. Divide this number into leading and trailing
  digits.
• 3. Write down all possible sets of leading digits
  in order from the lowest to highest as a column.
  These are stems.
• 4. For each data value write down the first
  trailing digit on the line labeled by its leading
  digits. These are the leaves. One leaf for each
  data value.

3
STEM-AND-LEAF DISPLAYS

• Uses actual data values to create a graph (pulse
  rates of 39 Peruvian Indians)
• 52, 56, 60, 60, 60, 60, 60, 60, 64, 64, 64, 64,
  64, 64, 64, 68, 68, 68, 68, 72,
• 72, 72, 72, 72, 72, 72, 72, 74, 76, 76, 76, 76,
  80, 80, 84, 88, 88, 88, 92

• STEPS
• 1. Select a typical data value.
• 2. Divide this number into leading and trailing
  digits.
• 3. Write down all possible sets of leading digits
  in order from the lowest to highest as a column.
  These are stems.
• 4. For each data value write down the first
  trailing digit on the line labeled by its leading
  digits. These are the leaves. One leaf for each
  data value.

• 64

4
STEM-AND-LEAF DISPLAYS

• Uses actual data values to create a graph (pulse
  rates of 39 Peruvian Indians)
• 52, 56, 60, 60, 60, 60, 60, 60, 64, 64, 64, 64,
  64, 64, 64, 68, 68, 68, 68, 72,
• 72, 72, 72, 72, 72, 72, 72, 74, 76, 76, 76, 76,
  80, 80, 84, 88, 88, 88, 92

• STEPS
• 1. Select a typical data value.
• 2. Divide this number into leading and trailing
  digits.
• 3. Write down all possible sets of leading digits
  in order from the lowest to highest as a column.
  These are stems.
• 4. For each data value write down the first
  trailing digit on the line labeled by its leading
  digits. These are the leaves. One leaf for each
  data value.

• 64

Leading Digits Trailing Digits
6 4
5
STEM-AND-LEAF DISPLAYS

• Uses actual data values to create a graph (pulse
  rates of 39 Peruvian Indians)
• 52, 56, 60, 60, 60, 60, 60, 60, 64, 64, 64, 64,
  64, 64, 64, 68, 68, 68, 68, 72,
• 72, 72, 72, 72, 72, 72, 72, 74, 76, 76, 76, 76,
  80, 80, 84, 88, 88, 88, 92

• STEPS
• 1. Select a typical data value.
• 2. Divide this number into leading and trailing
  digits.
• 3. Write down all possible sets of leading digits
  in order from the lowest to highest as a column.
  These are stems.
• 4. For each data value write down the first
  trailing digit on the line labeled by its leading
  digits. These are the leaves. One leaf for each
  data value.

• 64

Leading Digits Trailing Digits
6 4
Leading Digits Trailing Digits
6 4

• 5
• 6
• 7
• 8
• 9

6
STEM-AND-LEAF DISPLAYS

• Uses actual data values to create a graph (pulse
  rates of 39 Peruvian Indians)
• 52, 56, 60, 60, 60, 60, 60, 60, 64, 64, 64, 64,
  64, 64, 64, 68, 68, 68, 68, 72,
• 72, 72, 72, 72, 72, 72, 72, 74, 76, 76, 76, 76,
  80, 80, 84, 88, 88, 88, 92

• STEPS
• 1. Select a typical data value.
• 2. Divide this number into leading and trailing
  digits.
• 3. Write down all possible sets of leading digits
  in order from the lowest to highest as a column.
  These are stems.
• 4. For each data value write down the first
  trailing digit on the line labeled by its leading
  digits. These are the leaves. One leaf for each
  data value.

• 64

Leading Digits Trailing Digits
6 4
Leading Digits Trailing Digits
6 4

• 5
• 6
• 7
• 8
• 9

• 5 26
• 6 00000044444448888
• 7 2222222246666
• 8 004888
• 9 2

7
VERSIONS OF STEM-AND-LEAF DISPLAYS
Two-stem Display (2 lines per stem) Leaves 0,
1, 2, 3, 4 . 5, 6, 7, 8, 9
Five-stem Display (5 lines per stem) Leaves 0
, 1 t 2, 3 f 4, 5 s 6, 7 . 8, 9
8
VERSIONS OF STEM-AND-LEAF DISPLAYS

• 5 26
• 6 00000044444448888
• 7 2222222246666
• 8 004888
• 9 2

Two-stem Display (2 lines per stem) Leaves 0,
1, 2, 3, 4 . 5, 6, 7, 8, 9

• 5 2
• 5 6
• 6 0000004444444
• 6 8888
• 7 222222224
• 7 6666
• 8 004
• 8 888
• 9 2

• INTERPRETATION
• Center (typical observations)
• Spread (variation, minimum and maximum
  observations)
• Shape (symmetry, number of peaks, skewness)
• Other (unusual observations in the data set

9
BACK-TOBACK STEM-AND-LEAF DISPLAYS
Weights of 50 college students that were obtained
from their medical reports.
Female
Male

• 9 8
• 10 188
• 11 0255688
• 12 00089
• 13 257
• 14 2358
• 15 044578
• 16 122578
• 17 00667
• 18 3468
• 19 0155
• 20 5
• 21 5

• 9
• 10
• 11
• 12
• 13
• 14 358
• 15 044578
• 16 122578
• 17 00667
• 18 3468
• 19 0155
• 20 5
• 21 5

• 8
• 188
• 0255688
• 00089
• 257
• 2