Measures of Central Tendency for Ungrouped Data

1
Measures of Central Tendency for Ungrouped Data

• Section 3.1

2
Mean

• Mean Sum of all Values
• Number of Values
• Mean from a sample is x ?x/n
• Mean from population is µ ?x/N
• Mean is very sensitive to outliers.

3
Identity Fraud Victims in 2004 for Six States
4
Table 3.2 (p. 77)Total Philanthropic Givings in
Lifetime
5
Median

• Middle term of data after ranked in increasing
  order.
• Divides data into two equal parts.
• Not influenced by oultiers.

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Number of Car Thefts in 2003 in 12 Cities
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Mode

• Value with the highest frequency in a data set.
• Not all data sets have a mode.
• Some data sets have more than one mode.
• Unimodal One mode.
• Bimodal Two modes.
• Multimodal More than two modes.

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Comparisons of Measures of Center

• Mean is most common and each member of the data
  set is used in its calculation.
• Median is better if the data set contains
  outliers.
• Mode is the easiest to locate, but not much use.

9
Mean, median, and mode for a symmetric histogram
and frequency distribution curve.
10
Mean, median, and mode for a histogram and
frequency distribution curve skewed to the right.
11
Mean, median, and mode for a histogram and
frequency distribution curve skewed to the left.