# 1.2 Describing Distributions with Numbers - PowerPoint PPT Presentation

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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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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.

### 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.

### Median:

=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

• 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

• 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

• 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

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

Min M Max

18.5

Min M Max

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

• Measures spread by looking at how far the observations are from the mean.

• Denoted by s

• ** 1 – Var stats / Sx

### 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

### Example 5: Find the standard deviation for the set of data

*** 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