1 2 describing distributions with numbers
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1.2 Describing Distributions with Numbers. Describe the Histogram in terms of center, shape, spread, and outliers???. The most common measure of center (A.K.A. average) Denoted by The Mean is considered Non-resistant because it is sensitive to extreme values. May or may not be outliers .

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The most common measure of center (A.K.A. average)

  • Denoted by
  • The Mean is considered Non-resistant because it is sensitive to extreme values. May or may not be outliers.
  • On Calculator use 1 Var Stat to get the mean.
Mean:
median

The middle value of the set of data

  • Denoted as M
  • If the # of observations is odd, the median is the center observation.
  • If the # of observations is even then take the mean of the two center observations.
  • Median is resistant to extreme values
  • On Calculator use 1 Var Stat to get the median.
Median:
example 1 find and m for the set of data

=41.3 M=34

Example 2: Find and M for the set of data

Example 1: Find and M for the set of data

=19.1 M=18.5

comparison of and m

If……

            • Symmetrical – then they are very similar (close in value)
            • Skewed – Then is farther out in the tail than the median
            • Exactly symmetrical – exactly the same
Comparison of and M
measuring spread range the quartiles

Range = Largest Value – Smallest Value

  • - Lower Quartile – median of the observations smaller than the median
  • - Median
  • - Upper Quartile - median of the observations larger than the median
  • – Interquartile Range
      • Outliers fall more than below or above

** 1 – Var stats on your Calculator gives them all to you.

Measuring Spread: Range & the Quartiles
5 number summary

The 5# Summary consists of the smallest and largest observations from a set of data along with .

  • The 5# summary leads to a new graph called the box and whisker plot (boxplot).
  • Best used for comparing two sets of data
5 – Number Summary
properties of standard deviation

s measures spread about the mean and should be used only when the mean is used.

  • As s gets larger the observations are more spread out from the mean
  • s is highly influenced by outliers
Properties of Standard Deviation
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*** 5# Summary is usually better than the mean and standard deviation for describing a skewed distribution. Use the mean and standard deviation for data that is reasonably symmetric

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