STAT-S 300 Lecture Notes - Lecture 2: Histogram, Unimodality, Interquartile Range
Section 1.2-1.3 Notes- Displaying Quantitative Data with Graphs and Describing Quantitative
Data with Numbers 8-9-13 thru 8-15-13
• Graphs for Quantitative Data
o Dot Plot
o Histogram
▪ Minimum 5 classes
▪ If on line between classes, data point goes in higher class
▪ Relative frequency (%) easier to compare to distributions
▪ Find median- use frequency
o Box Plot
▪ Central box- Q1 to Q3
• Line marks Q2
▪ Lines (whiskers) extend from box to min and max
• First calculate outliers, if any, put as dots and extend whiskers to
next non-outlying value
o Stem Plot/Stem-and-Leaf Plot
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0
5
1
0 2 3
2
6
3
1 2 9
4
4 7
5
8 8 9
▪ Do not use for large sets or large values (truncate)
▪ Min. 5 stems
▪ Splitting and back-to-back for comparing
▪ Give quick picture of shape of distribution while including actual
numerical values in graph
▪ Steps to Making a Stem Plot
• Separate each observation into a stem, consisting of all but the
final digit, and a leaf, the final digit
• Write the stems in a vertical column in numerical order, going
down
• Draw a vertical line at the right of this column
• Do not skip any stems, even if there is no data value for a
particular stem
• Write each leaf in the row to the right of its stem
• Arrange the leaves in increasing order out from the stem
• Provide a key that explains in context what the stems and leaves
represent
o 3 | 6 = 36
▪ Splitting stems- two of each stem, 0-4 on first, 5-9 on second
• Helps get better picture of data for cases with few stems and many
leaves
• If splitting stems, make sure each stem can have an equal number
of leaves (ex. 2 stems, 5 leaves each; 5 stems, 2 leaves each)
▪ Back-to-back stem plot- common stem, two sets of leaves (ex. number of
pairs of shoes for students, split into males and females)
• Leaves on each side ordered out from common stem
▪ If data has too many digits, round to get simple stems and leaves (ex.
$42,549 should be rounded to $43,000 for stem 4 and leaf 3)
• Purpose of graphs is to help understand data
o How to Examine the Distribution of a Quantitative Variable
▪ In any graph, look for the overall pattern and for striking departures
from that pattern
• You can describe the overall pattern of a distribution by its shape,
outliers, center, and spread (SOCS)
o Shape- main visual features of graph(s)
▪ Irrelevant for graphs of categorical variables
▪ Known as mode (ex. look for highest value on
dotplot)
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