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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.
- On Calculator use 1 Var Stat to get the mean.

- 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.

=41.3 M=34

Example 2: Find and M for the set of data

=19.1 M=18.5

- 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

- 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.

- Outliers fall more than below or above

- 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

- Therefore, the observations 85 and 86 are both outliers for the set of data.

Min M Max

18.5

Min M Max

- Measures spread by looking at how far the observations are from the mean.
- Denoted by s
- ** 1 – Var stats / Sx

- 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

*** 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