1 / 25

Measures of Central Tendency

Measures of Central Tendency. Quiz 1 vs. Retake. Mode. The most frequently occurring score in a data set. Can be any type of data (nominal, ordinal, etc.). Mode. Using a frequency distribution table, you can easily find the mode.

starr
Download Presentation

Measures of Central Tendency

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. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Measures of Central Tendency

  2. Quiz 1 vs. Retake

  3. Mode • The most frequently occurring score in a data set. • Can be any type of data (nominal, ordinal, etc.)

  4. Mode • Using a frequency distribution table, you can easily find the mode. • Scan the frequency column for the highest number, then see what score it is associated with.

  5. Mode • What if two scores have the highest frequency? • Then you have a “bimodal” data set, and you report both modes. • 3+ modes = multimodal • It is also possible to have a data set with no mode. (Ex: 3, 7, 6, 1) M F

  6. What is the Mode? Birthdays in: • January – March • April – June • July – September • October – December

  7. Median • The “middle score” in a data set. • The point along the score scale that separates the top 50% of the scores from the bottom 50% (the score value at the 50thpercentile). • The ___th percentile is the score at or below which ___% of the scores lie.

  8. Finding the Median (Odd Number of Scores) 2, 3, 5, 6, 7, 8, 9 6, 3, 9, 2, 5, 7, 8 Step 1: Put the scores in order. Step 2: Calculate the position of the median by using the formula (N + 1)/2 (in this case, the 4th position). Step 3: The median is the value of the score in that position (in this case, 6).

  9. Finding the Median (Even Number of Scores) 2, 3, 4, 5, 6, 7, 8, 9 4, 8, 2, 9, 3, 5, 7, 6 Step 1: Put the scores in order. Step 2: Calculate the position of the score before the median by using the formula N/2 (in this case, the 4th position). Then calculate the position of the score after the median by using the formula N/2 + 1 (in this case the 5th position). Step 3: Calculate the average of the two scores surrounding the median (in this case (5 + 6)/2 = 5.5). This is the median. 5.5

  10. Finding the Median • Remember, it is easy to find the mean with a cumulative frequency distribution table. • In this example, there are 149 scores, and (149 + 1)/2 = 75. • We look for 75 or the closest number larger than 75 in the Cum f column. • The median is the corresponding X value. In this example, it is 72 BPM. • What do you do if the median score in an even data set is between two X values? Calculate the average.

  11. Mean ( ) • The sum of scores in a distribution divided by the number of scores. • For a sample: • For a population:

  12. Mean • If you have a frequency distribution, create a new column, fX. • Multiply the X value by the frequency score for each row to get the fX value. • Sum the f column (for N) and the fX column. • Divide the sum of fX by N (the sum off).

  13. Range • The range is the difference between the highest score (HS) in the distribution and the lowest score (LS). • Ex: The range of the numbers 4, 8, 2, 9, 3, 5, 7, 6 is calculated by subtracting 2 from 9, which is equal to 7.

  14. Activity #1 • Find the mean, median, mode, and range of the following data: • 25, 93, 21, 21, 86, 91, 35, 95, 90, 22, 26, 19, 85, 99, 88, 24, 30, 31, 91, 29, 89, 37, 83, 91, 27, 91, 21, 30, 44, 97, 99, 21, 92, 84, 86, 32 • Put your name on your paper.

  15. Deviation • Make sure you understand this concept! • The difference between a score and the mean of the scores in a distribution.

  16. Mean as a Balancing Point • The sum of the differences between X and the mean will always be 0. -3 -1 +4

  17. Deviation with a Frequency Distribution • Create another column by multiplying the deviation score by the frequency score. • The sum of these scores should always be zero.

  18. Average Deviation • Since the average deviation always produces a result of 0, how can it every be useful? • By using the following formula instead, we can find the average distance (AD) of each score from the mean. • This can be a useful measure.

  19. Where are the Measures? Mean? Median? Mode?

  20. Which One Should You Use? • Mode • When you have nominal data • When you are interested in which score occurred most frequently • Median • When you have a seriously skewed distribution • When your data set is cut off at an arbitrary value • Mean • When you are interested in the population mean • When you want a reliable measure based on all of the data

  21. Why Use Measures of Central Tendency? • They are easy to remember and look at. • Ex: Retake Quiz Scores Summary Measures: • Mean: 15.4 • Median: 16.5 • Mode: 18 • σ: 4.48 (we will talk about this next week)

  22. But There are Risks • Summary data from Activity #1: • Mean: 59 • Median: 63.5 • Mode: 21 and 91 • Range: 80

  23. But Look at the Histogram Mean Mode Mode Median

  24. What’s the Take Home Message? • Always look at the data in graphical form. • You are trying to paint a picture with your data analysis, a picture that demonstrates your point but is an accurate representation of what you found. • Make sure that your summary measures are accurate representations of your data.

  25. Homework • Study for Chapter 5 Quiz • (don’t forget about range and AD from chapter 6) • Read Chapter 6 • Do Chapter 5 Homework

More Related