1 / 16

Lecture Outline 3

Lecture Outline 3. Measures of Central Tendency Please note: Not all slides/material from the lectures are included here. This presents only a detailed outline of the lecture. Measures of Central Tendency. Three main types Mode Median Mean Choice depends upon level of measurement.

Download Presentation

Lecture Outline 3

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. Lecture Outline 3 Measures of Central Tendency Please note: Not all slides/material from the lectures are included here. This presents only a detailed outline of the lecture.

  2. Measures of Central Tendency • Three main types • Mode • Median • Mean • Choice depends upon level of measurement

  3. The Mode • The mode is the most frequently occurring value in a distribution. • Abbreviated as Mo • EX: 20, 21, 30, 20, 22, 20, 21, 20 (Mo?) • Sometimes there is more than one mode • EX: 96, 91, 96, 90, 93, 90, 96, 90 • Bimodal • Mode is the only measure of central tendency appropriate for nominal-level variables

  4. The Median Position of the Mdn • The median is the middle case of a distribution • Abbreviated as Mdn • Appropriate for ordinal or interval level data • How to find the median? • If even, there will be two middle cases – interpolate • If odd, choose the middle-most case • Cases must be ordered • Multiple identical values in the middle • – Numerical value becomes the median

  5. What is the median? odd or even? (7+1)/2=4th case Where is the 4th case? Sort distribution from lowest to highest 1 5 2 9 13 11 4 Example of median: Years in Marriage Position of the Mdn

  6. 4th case? 5 years=Mdn Interpretation? 1 2 4 5* 9 11 13 Example of median: Years in Marriage

  7. What is the median? (8+1)/2=4.5 Half way between the 4th and 5th case Mdn=2.5 2.5 years Interpretation? 1 1 2 2 3 4 4 6 Example of median with 8 cases Position of the Mdn

  8. The Mean • The mean is appropriate for interval and ratio level variables X = raw scores in a set of scores N = total number of scores in a set

  9. Mdn Mo Step-by-step Illustration: Mode, Median, and Mean Suppose that a volunteer contacts friends on campus collecting for a local charity. She receives the following donations (in Liras): 5 10 25 15 18 2 5 Step 1: Arrange the scores from highest to lowest. Step 2: Find the most frequent score. Mo = 5 Step 3: Find the middlemost score. Mdn = 10 25 18 15 10 5 5 2

  10. Step-by-step Illustration: Mode, Median, and Mean Step 4: Determine the sum of scores. Step 5: Determine the mean by dividing the sum by the number of scores. 25 18 15 10 5 5 2 ∑X = 80

  11. Comparing the Mode, Median, and Mean • Three factors in choosing a measure of central tendency • Level of measurement • Shape or form of the distribution of data • Research Objective

  12. Level of Measurement

  13. Shape of the Distribution • In symmetrical distribution – mode, median, and mean have identical values • In skewed data, the measures of central tendency are different • Skewness relevant only at the interval level • Mean heavily influenced by extreme outliers • median best measure in this situation

  14. Research Objective • Choice of reported central tendency depends on the level of precision required. • Most published research requires median and/or mean calculations. • In skewed data, report mean and median together to understand where the skew is.

  15. Figure 1 This figure shows the relative positions of the mean and median for right-skewed, symmetric, and left-skewed distributions. Note that the mean is pulled in the direction of skewness, that is, in the direction of the extreme observations. For a right-skewed distribution, the mean is greater than the median; for a symmetric distribution, the mean and the median are equal; and, for a left-skewed distribution, the mean is less than the median.

More Related