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Summarizing and Displaying Data
Chapter 2
Goals for Chapter 2

To illustrate:
– A summary of numerical data is more easily
comprehended than the list itself
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To explain:
– the shape of the distribution of numerical data; terms
used to describe this shape.

To learn:
– how to construct stem-and-leaf plots, histograms; numerical
values to summarize data
– center of data distribution: mean, median, mode
– variability of data distribution: range, interquartile range,
standard deviation

To discuss:
– what kinds of summaries are best for various measurements
Thought Question 1:
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Salaries of male and female employees are being
compared to see if discrimination exists.
How would you present the data ?
Thought Question 2:
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Suppose you are comparing two job offers and one
of your considerations is the cost of living in each
area. You get the local newspapers and record the
price of 50 advertised apartments for each
community.
How would you summarize the rent values for
each community in order to make a useful
comparison?
Thought Question 3:
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Your boss wants to find out whether your company
spends appreciably more on direct mail advertising
than other companies of the same size in the
industry.
What data would you present and how?
Thought Question 4:
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Your boss wants to find out whether there is a direct
relation between gross annual sales and annual
expenditures for direct mail advertising for
companies like yours.
What data would you present and how?
Types of Data
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Qualitative--”Categorical”
– Answer “Yes” or “No”; “Male” or “Female”; “Sick” or
“Healthy”; hair color.
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Quantitative--”Measurement”
– Discrete (integer values): counting, ordering
– Continuous (example): height, weight,
Three Properties of a Set of Data
(Distribution):

1. The center location
– described by mean, median or mode
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2. The variability
– described by range, interquartile range (IQR), standard
deviation
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3. The shape
– symmetric (the same on either side of the center--mean,
median and mode are the same value)
– skewed (different on one side of center, mean different from
mode different from median)
Definitions for Center (Location)

Mean: average of values:
– xmean= xbar = ( xi) / N, where values of xi go over
all N values in sample.

Median: Value of xi that is in the middle of the
ordered values:
– xmedian = x(N+1)/2 if N is odd;
– xmedian = (xN/2 + xN/2+1 )/2 if N is even;
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Mode: most frequent value
Measures of Variability
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Range: difference between minimum and
maximum values:
– range = xN - x1
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Interquartile Range (IQR): contains 50% of
values (25% below median, 25% above).
– IQR = Q3 - Q1
– Q1 is first quartile value; Q3 is third quartile value
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Variance: measure of average square variation
from mean;
Standard Deviation: square root of variance.
Example--Ex02.11: Production Data.
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Production per shift (maximum is 720 cars /shift):
– 688, 711, 625, 701, 688, 667, 694, 630, 547, 703, 688,
697, 703, 656, 677, 700, 702, 688, 691, 664, 688, 679,
708, 699, 667.

Production values--ordered
– 547, 625, 630, 656, 664, 667, 667, 679, 688, 688, 688,
688, 688, 691, 694, 697, 699, 700, 701, 702, 703, 703,
703, 708, 711
Example--Ex02.11: Production Data-2.

Stem -and-leaf diagram of Production Data
Leaf Unit = 10, N=26
1
5 4
1
5
1
5
1
6
3
6 23
4
6 5
9
6 66677
(9)
6 888889999
8
7 00000001
Example--Ex02.11: Production Data-3.
Leaf Unit = 10, N=26
1
5 4
1
5
1
5
1
6
3
6 23
4
6 5
9
6 66677
(9)
6 888889999
8
7 00000001
MEDIAN: 68x (688); Q1: 66x (667); Q3: 70x (701);
25% of the values (6.5) are below Q1, 25% above Q3;
50% of the values are below the median, 50% above.
Production Data--Boxplot
Production
Edges of box are at
Q1 and Q3;
whiskers extend
1.5*std.dev from
edges or until
max or min
value; note
outlier (“*”)
700
650
600
550