GES 255

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GES 255

• Engineering Statistics I

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Material

• Chapter 1 Overview and Descriptive Statistics.
• Section 1.3 Measures of Location.
• Mode.

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Mean

• The sample mean is denoted by .
• The population mean is denoted by ?.
• Equation

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Mean

• EX02 - Sec.1.3 (Excel and Minitab).
• The mean is the balance point for a set of data.
• The mean is affected by outliers, which are
  unusually small or large data values when
  compared to the rest of the data in the sample.

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Median

• The sample median is denoted by .
• The population median is denoted by .
• The median is the middle value of an ordered data
  set.
• If n is odd, then is the middle value.
• If n is even, then is the mean of the two
  middle values.

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Median

• EX02 - Sec.1.3 (Excel and Minitab).
• An advantage the median has over the mean is its
  insensitivity to outliers.
• A disadvantage is the median only uses one or two
  values in the sample (the mean uses all n values
  in the sample).

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Trimmed Mean

• A compromise between and .
• Denoted by .
• Disregards only a certain percentage (e.g., 10,
  20) of the smallest and largest values in an
  ordered data set.
• It is calculated as the mean of the remaining
  values after trimming.
• EX02 - Sec.1.3 (Excel and Minitab (5)).

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Quartiles

• Divide an ordered data set into four equal parts.
• The first quartile (Q1) separates the lower 25
  of the data from the upper 75.
• The second quartile (Q2) is .
• The third quartile (Q3) separates the lower 75
  of the data from the upper 25.
• EX02 - Sec.1.3 (Minitab).

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Percentiles

• Divide an ordered data set into 100 equal parts.
• The 99th percentile separates the lower 99 of
  the data from the upper 1.
• The 98th percentile separates the lower 98 of
  the data from the upper 2.
• And so on.
• We will see percentiles in Chapter 4.

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Categorical Dataand Sample Proportions

• Categorical data is data that can be divided into
  categories.
• For example, undergraduate students at UA can be
  categorized as freshmen, sophomores, juniors, or
  seniors.
• A sample proportion is denoted by x/n.
• A population proportion is denoted by p.

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Mode

• The mode is the data value that occurs most often
  in a data set.
• EX02 - Sec.1.3 (Excel).

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Symmetry and Skewness

• If the data in the sample are symmetric, then
  mean median mode.
• If the data in the sample are skewed left, then
  usually mode gt median gt mean.
• If the data in the sample are skewed right, then
  usually mode lt median lt mean.
• Histogram transparency.

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The End!

• That is it for Section 1.3
• Measures of Location Mode