1 2 describing distributions with numbers
This presentation is the property of its rightful owner.
Sponsored Links
1 / 14

1.2 Describing Distributions with Numbers PowerPoint PPT Presentation


  • 55 Views
  • Uploaded on
  • Presentation posted in: General

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 .

Download Presentation

1.2 Describing Distributions with Numbers

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


1 2 describing distributions with numbers

1.2 Describing Distributions with Numbers


1 2 describing distributions with numbers

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


1 2 describing distributions with numbers

  • 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


Example 3 find any outliers for the set of data

  • Therefore, the observations 85 and 86 are both 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 M Max

18.5

Min M Max

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


Standard deviation

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

  • Denoted by s

  • ** 1 – Var stats / Sx

Standard Deviation


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


Example 5 find the standard deviation for the set of data

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


1 2 describing distributions with numbers

*** 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


  • Login