Descriptive Statistics

1
Descriptive Statistics

• Statistical Notation
• Measures of Central Tendency
• Measures of Variability
• Estimating Population Values

2
Statistical Notation

• Statistics for populations are called parameters
  and are represented with Greek letters (m, s).
• Statistics for samples are called statistics and
  are represented with English letters (M, SD).

3
Summation Notation

• The capital Greek letter S means sum of
• Sx means add up all the scores on variable x
• If the scores on x are 2, 3, 5, Sx 10

4
Measures of Central Tendency

• Indicates the typical score in a distribution
• Mean (M, m) is the arithmetic average
• Median (Mdn) is the middle score (50th ile)
• Mode is the most common score

5
Measures of Central Tendency

• The mean requires interval/ratio data affected
  by all scores can be distorted by outliers.
• The median requires ordinal or higher level data
  not distorted by outliers.
• The mode can be used with any type of data
  unstable in small samples.

6
Measures of Variability

• Indicate spread of scores
• The range is the difference between the highest
  and lowest scores.
• The standard deviation (SD, s) is average
  distance from the mean.
• The variance (s2, s2) is the average squared
  distance from the mean.

7
Measures of Variability

• The range can be unstable in small samples.
• Standard deviation is the most commonly used
  measure of variability.
• Variance is difficult to interpret because it is
  in squared units, but is used in inferential
  statistics.
• All measures require interval/ratio data.

8
Estimating Population Values

• We are sometimes interested in estimating
  descriptive statistics for a population based on
  a sample.
• The best estimate of the population mean is the
  sample mean.
• The sample mean is an unbiased estimate.

9
Estimating Population Values

• The best estimate of the population s is not the
  sample s.
• The sample s tends to underestimate the
  population s it is a biased estimate.
• The formula for estimated population standard
  deviation compensates for this bias.