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PStem-and-leaf plot = a histogram-like display of a batch of
numbers(“distribution”)
< Stem = axis = first one or two digits
< Leaves = data points = next significant digit ( n leaves)
PIllustrative data set #1 (SAMPLE.SAV, AGE variable, n = 10)
< Ordered array : 05 11 21 24 27 28 30 42 50 52
P Data point 21 is shown as:
Chapter 2: Frequency Distributions
p. 2.
|5| |4| |3| |2| |1| |0| AGE(x 10)
Stem-and-LeafPlot
Full plot: SAMPLE.SAV, AGE (years, n = 10)
(x 10) 7 axis multiplier
Interpretationof Stem Plots
p. 2.2 (Stem-and-leaf rotated 90
o
Age (x10)
P Shape
P Location
P Spread
PSymmetry?
PMound(s)?
Interpretation
Shape
X
X
X X
X X X X X X
0 1 2 3 4 5 (x10)
Difficult to make shape statements when n small
PData: 1.47 2.06 2.36 3.43 3.74 3.78 3.94 4.
PTruncate third digit (e.g., 1.47 6 1.4)
PPloteachpoint:
Second Illustrative Data Set
p. 2.
(x 1)
P Regular plot 6 too squished to show shape, location, spread
|1| |2| |3| (x 1)
P Double-stem values 6 does a better job showing distribution
< Leaves 0 - 4 on first stem value, 5 - 9 on second
(x 1)
Third
pollution levels in river water (p. 2.3)
SPSS
Then
More on What to Look for...
p. 2.
Histogram curve
Kurtosis
p. 2.
(A) Mesokurtic (B)Platykurtic
C) Leptokurtic
Location (p. 2.7)
PCenter = average = summary of
location
PYou
0.4 Group
Spreads
(p. 2.8)
Population 1
Population 2
F 1 F^2
PDeviation (F) around center as a
summary
PYou
Can you describe this
distribution?
Exercise 2.5 (%IDEAL, n = 18)
| 8| | 9| |10| |11| |12| |13| |14| |15| (% of ideal body wt x 10)
Ungrouped
p. 2.9 (Example: FEV.sav AGE variable)
AGE | Freq RelFreq. CumRelFreq ------+----------------------- 3 | 2 0.3% 0.3% 4 | 9 1.4% 1.7% 5 | 28 4.3% 6.0% 6 | 37 5.7% 11.6% 7 | 54 8.3% 19.9% 8 | 85 13.0% 32.9% 9 | 94 14.4% 47.2% 10 | 81 12.4% 59.6% 11 | 90 13.8% 73.4% 12 | 57 8.7% 82.1% 13 | 43 6.6% 88.7% 14 | 25 3.8% 92.5% 15 | 19 2.9% 95.4% 16 | 13 2.0% 97.4% 17 | 8 1.2% 98.6% 18 | 6 0.9% 99.5% 19 | 3 0.5% 100.0% ------+----------------------- Total | 654 100.0%
P Decide on no. of intervals (usually, 4 - 12)
< SAMPLE.SAV, AGE : 05 11 21 24 27 28 30 42 50 52
< Say, 4 class intervals
P Interval width. (max − min) / (no. intervals)
< width. (52 - 5) / 4 = 11.
< Use practical widths, e.g, 15-year class intervals
P Set endpoint conventions
< Let’s include left-endpoint and exclude right-endpoint
< First interval is 0 - 14 ( not 0 - 15)
P Count and tabulate
GroupedData,Uniform Intervals
p. 2.
GroupedData,Uniform Intervals
p. 2.
Range Tally Freq. RelFreq CumRelFreq
0-14 // 2 20% 20% 15-29 //// 4 40% 60% 30-44 // 2 20% 80% 45-59 // 2 20% 100%
TOTAL 10 100% –
PUse
Pe.g., FEV.SAV, AGE
Non-Uniform
p. 2.
AGEGRP (years) | Freq Percent Cum. ---------------+----------------------- PRESCHOOL (3-4)| 11 1.7% 1.7% ELEM (5-11) | 469 71.7% 73.4% MIDDLE (12-13) | 100 15.3% 88.7% HIGH (14+) | 74 11.3% 100.0% ---------------+----------------------- Total | 654 100.0%
Bar Charts w/ Noncontiguous
Bars
Use with Ordinal and Nominal Groups
Age
Pre-sch Elem-Sch Mid-Sch High-sch
0
100
200
300
400
500
Group 2
FIGURES FOR TEXT
