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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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Mean:


Median

  • The middle value of the set of data and outliers???

  • 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 and outliers???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…… and outliers???

    • 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 and outliers???

  • - 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

5 – Number Summary


Example 3 find any outliers for the set of data

Example 3: Find any outliers for the set of data.


Example 4 create a boxplot for each set of data what can you conclude

Min the set of data. M Max

18.5

Min M Max

Example 4: Create a boxplot for each set of data. What can you conclude?


Standard deviation

Standard Deviation


Properties of standard deviation

  • s from the mean. 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



*** 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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