Measures of Central Tendency (MCT)

1
Measures of Central Tendency (MCT)

1. Describe how MCT describe data
2. Explain mean, median mode
3. Explain sample means
4. Explain deviations around mean

2
More Statistical Notation

• An important symbol is ?, it is the Greek letter
  ? called sigma
• This symbol means to sum (add)
• You will see it used in notations such as ? X.
  This is pronounced as the sum of X and means to
  find the sum of the X scores

3
Why Is It Important to Knowabout MCT?
4
Central Tendency

• MCT answer the question
• Are the scores generally high scores or
  generally low scores?
• What are they?
• A MCT is a score that summarizes the location of
  a distribution on a variable
• It is the score that indicates where the center
  of the distribution tends to be located

5
The Mode

• The most frequently occurring score is called the
  mode
• The mode is typically used to describe central
  tendency when the scores reflect a nominal scale
  of measurement

6
Unimodal Distributions

• When a polygon
• has one hump (such as on the normal curve) the
• distribution is called unimodal.

7
Bimodal Distributions

• When a distribution
• has two scores that
• are tied for the most
• frequently occurring
• score, it is called
• bimodal.

8
The Median
9
The Median

• The median (Mdn) is the score at the 50th
  percentile
• The median is used to summarize ordinal or highly
  skewed interval or ratio scores

10
Determining the Median

• When data are normally distributed, the median is
  the same score as the mode.
• When data are not normally distributed, follow
  the following procedure
• Arrange the scores from lowest to highest.
• If there are an odd number of scores, the median
  is the score in the middle position.
• If there are an even number of scores, the median
  is the average of the two scores in the middle.

11
The Mean
12
The Mean

• The mean is the score located at the exact
  mathematical center of a distribution
• The mean is used to summarize interval or ratio
  data in situations when the distribution is
  symmetrical and unimodal

13
Determining the Mean

• The formula for the sample mean is

14
Sample Mean versus Population Mean

• is the sample mean. It is a sample
  statistic.
• The mean of a population is a parameter. It is
  symbolized by m (pronounced mew).
• is used to estimate the corresponding
  population mean m.

15
Central Tendency and Normal Distributions
On a perfect normal distribution all three
measures of central tendency are located at the
same score.
16
Central Tendency andSkewed Distributions
17
Deviations Aroundthe Mean
18
Deviations

• A scores deviation is equal to the score minus
  the mean.
• In symbols, this is
• The sum of the deviations around the mean
  always equals 0.

19
More About Deviations

• When using the mean to predict scores, a
  deviation indicates our error in prediction.
• A deviation score indicates a raw scores
  location and frequency relative to the rest of
  the distribution.