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1.2 Describing Distributions with Numbers

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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1.2 Describing Distributions with Numbers

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  1. 1.2 Describing Distributions with Numbers

  2. Describe the Histogram in terms of center, shape, spread, and outliers???

  3. 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:

  4. 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:

  5. =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

  6. 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

  7. 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

  8. 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

  9. Therefore, the observations 85 and 86 are both outliers for the set of data. Example 3: Find any outliers for the set of data.

  10. Min M Max 18.5 Min M Max Example 4: Create a boxplot for each set of data. What can you conclude?

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

  12. 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

  13. Example 5: Find the standard deviation for the set of data

  14. *** 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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