Histograms & Stemplots
for Quantitative Data
Describing Data using
Summary Features of Quantitative
Variables
Center—Location in middle of all data
Unusual features - Outliers, gaps, clusters
Spread—Measure of variability, range
Shape—Distribution pattern: symmetric, skewed,
uniform, bimodal, etc.
CUSS in context!
Dotplot for Univariate
Quantitative Data
Center: about -50
Unusual features:
gap at -45
Spread: 48 degrees
(-69 to -21)
Shape: trimodal,
representing 3
seasons
Stemplot for Quantitative Data
Ages of Death of U.S. First Ladies
3
4
5
6
7
8
9
|
|
|
|
|
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|
4,
3
2,
0,
0,
1,
7
6
4,
0,
1,
1,
Key
5,
1,
3,
2,
7,
2,
4,
3,
3 | 4 indicates 34 years old
8
4, 4, 4, 5, 6, 9
6, 7, 8, 8
3, 6, 7, 8, 9, 9
Stem
Leaf—a
single digit
Center: 65 years, Spread: 63 years;
Shape: skewed left (towards lower numbers)
How to make a Stemplot
(Stem and Leaf Plot)

Separate each observation into a stem (all but
the last digit) and a leaf (the last digit)



Sometimes rounding to the nearest hundred,
thousand, etc. is a good idea when there are a lot of
digits to consider
Write the stems in a vertical column in order
from smallest to largest and draw a vertical line
at the right of the column
Write each leaf in the row to the right of its
stem in increasing order
Make a stemplot with the
following data

Joey’s first 14 quiz grades in a marking
period were:
86
87
7
8
9
84
76
4568
02467
01368
91
96
75
82
78
90
80
98
74
93
Key: 7 | 4 is score of 74
Center: 86; Spread: 24; Shape: Uniform
Split Stemplot
Stem is split
for every 2
leaves—
(0, 1), (2, 3),
(4, 5), (6, 7),
and (8, 9)
1
1
2
2
2
2
2
3
|
|
|
|
|
|
|
|
7
8,
0,
2,
4,
9, 9, 9, 9, 9
0, 0, 0, 1, 1, 1, 1, 1, 1
2, 2, 3, 3
5
8
0, 1
Age of 27 students randomly selected from Stat 303 at A&M
Split Stemplot
1
1
2
2
3
3
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|
|
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7, 8, 9, 9, 9, 9, 9
0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4
5, 8
0, 1
Stem is split for every 5
leaves—(0 thru 4) and
(5 thru 9)
Age of 27 students randomly selected from Stat 303 at A&M
Back-to-back Stemplot
Babe Ruth
When comparing
|0|
data, use comparative
|1|
language! (higher,
more than, etc.)
5, 2 | 2 |
5, 4 | 3 |
9, 7, 6, 6, 6, 1, 1 | 4
9, 4, 4 | 5 |
0|6|
Roger Maris
8
3, 4, 6
3, 6, 8
3, 9
1
Number of home runs in a season
Compare Ruth & Maris

Who’s Better?


Any unusual features?


Maris has a possible outlier at 61
Spread?


Babe Ruth – centered higher at about 47 compared to
Maris at 23
Maris has larger spread of 53 compared to Babe’s of
38
Shape?

Babe’s is mound shaped and symmetrical, while
Maris’s is skewed right with the outlier
Histogram
Histogram
TX_betw eenHoustonDallas
120
Frequency Count
This bin represents the # of
people whose age is at least
20 but less than 25
100
Count
80
Centered at about 35
Skewed right
Spread of 90 years
60
40
20
0
20
40
Variable being counted
60
age
80
100
Uniform Distribution from
rolling a fair six-sided die 300
times
70
59
Frequency
60
50
54
42
54
46
45
3
4
40
30
20
10
0
1
2
Face of Fair Six-sided Die
5
6
How to make Histograms
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
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

Divide the list of data into groups or classes of
equal width (0-5, 5-10, 10-15, etc)
Scale the horizontal axis using these classes
Count the number of individuals in each class
Scale the vertical axis using the counts
Draw bars representing the count for each class,
so each bar has equal width
Histograms on the calculator





Enter data into List
Choose histogram option in StatPlot
Choose the list you used for Xlist
Choose 1 for Freq or a 2nd list if data is stored
in two lists (values in one, frequency in
another)
Zoom 9:statplot will scale it for you but check
the Window to make sure you have
reasonable values of min & max for both x
(values) and y (frequency count). The Xscl
will set the width of the bars.
Ch. 3 Test Results
Centered at
about 80
No unusual
features
Skewed left
Spread of about
60
Ch. 3 Test Results
Decimal point is 1 digit(s) to the right of
the colon.
4:4
4:9
5 : 13
5 : 589
6 : 01111444
6 : 5666678
7 : 00012222233344
7 : 5666678888889999999
8 : 00112223333334444
8 : 56666668889999999
9 : 012222222334444
9 : 555667789
10 : 0
Make a histogram using Babe
Ruth’s data from the earlier slide