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Chapter 2
Describing, Exploring, and Comparing Data
Section 2.1 - Overview
Terms:
Center
Variation
Distribution
Outliers
Time
Section 2.2 – Frequency Distributions
Terms:
Frequency
Frequency Distribution
(lower and upper class limits, class boundaries, class midpoints, class width)
Relative Frequency
Relative Frequency Distribution
Cumulative Frequency
Cumulative Frequency Distribution
Cumulative Relative Frequency
Open-Ended Intervals
Section 2.3 – Visualizing Data
Read this section on your own.
Section 2.4 – Measures of Center
Notation:
n
x 
N
x
n
 
x
22
23.8
N
Terms:
Mean (arithmetic mean)
Median
Mode
Bimodal
Multimodal
Midrange
Weighted Mean
Skewed
Skewed to the left
Skewed to the right
Symmetric
Example – Exercise #3
17.7
19.6
19.6
20.6
21.4
24
25.2
27.5
28.9
29.1
29.9
33.5
37.7
40
42
Example – Exercise #5
14
16
17
18
20
21
23
24
25
27
28
30
31
34
37
38
Section 2.5 – Measures of Variation
Notation:
s
s2
σ
σ2
Terms:
Range
Standard Deviation of a Sample
Standard Deviation of a Population
Sample Variance
Population Variance
Coefficient of Variation
Mean Absolute Deviation (MAD)
Empirical Rule
For data sets having a distribution that is approximately bell-shaped, the following properties
apply
About ______ of all values fall within _____ standard deviation(s) of the mean
About ______ of all values fall within _____ standard deviation(s) of the mean
About ______ of all values fall within _____ standard deviation(s) of the mean
Chebyshev’s Theorem
The proportion (or fraction) of any set of data lying within K standard deviations of the mean
1
is always at least 1  2 , where K is any positive number greater than 1.
K
If K = 2, then at least _____ of all values fall within 2 standard deviations of the mean.
If K = 3, then at least _____ of all values fall within 3 standard deviations of the mean.
Section 2.6 – Measures of Relative Standing
Terms:
Standard Score (z Score)
Sample z 
xx
s
Quartiles
Percentiles
Interquartile Range (IQR)
Semi-interquartile Range
Midquartile
Population z 
x
