3. Descriptive statistics

# 3. Descriptive statistics - 3 Descriptive Statistics...

This preview shows pages 1–12. Sign up to view the full content.

3. Descriptive Statistics Describing data with tables and graphs (quantitative or categorical variables) Numerical descriptions of center, variability, position (quantitative variables) Bivariate descriptions (In practice, most studies have several variables)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Frequency distribution : Lists possible values of variable and number of times each occurs Example : Student survey ( n = 60) www.stat.ufl.edu/~aa/social/data.html “political ideology” measured as ordinal variable with 1 = very liberal, …, 4 = moderate, …, 7 = very conservative 1. Tables and Graphs

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Histogram : Bar graph of frequencies or percentages
Shapes of histograms (for quantitative variables) Bell-shaped (IQ, SAT, political ideology in all U.S. ) Skewed right (annual income, no. times arrested) Skewed left (score on easy exam) Bimodal (polarized opinions) Ex . GSS data on sex before marriage in Exercise 3.73: always wrong, almost always wrong, wrong only sometimes, not wrong at all category counts 238, 79, 157, 409

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Stem-and-leaf plot (John Tukey, 1977) Example : Exam scores ( n = 40 students) Stem Leaf 3 6 4 5 37 6 235899 7 011346778999 8 00111233568889 9 02238
2.Numerical descriptions Let y denote a quantitative variable, with observations y 1 , y 2 , y 3 , … , y n a. Describing the center Median : Middle measurement of ordered sample Mean : 1 2 ... n i y y y y y n n + + + Σ = =

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Example : Annual per capita carbon dioxide emissions (metric tons) for n = 8 largest nations in population size Bangladesh 0.3, Brazil 1.8, China 2.3, India 1.2, Indonesia 1.4, Pakistan 0.7, Russia 9.9, U.S. 20.1 Ordered sample: Median = Mean = y
Example : Annual per capita carbon dioxide emissions (metric tons) for n = 8 largest nations in population size Bangladesh 0.3, Brazil 1.8, China 2.3, India 1.2, Indonesia 1.4, Pakistan 0.7, Russia 9.9, U.S. 20.1 Ordered sample: 0.3, 0.7, 1.2, 1.4, 1.8, 2.3, 9.9, 20.1 Median = Mean = y

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Example : Annual per capita carbon dioxide emissions (metric tons) for n = 8 largest nations in population size Bangladesh 0.3, Brazil 1.8, China 2.3, India 1.2, Indonesia 1.4, Pakistan 0.7, Russia 9.9, U.S. 20.1 Ordered sample: 0.3, 0.7, 1.2, 1.4, 1.8, 2.3, 9.9, 20.1 Median = (1.4 + 1.8)/2 = 1.6 Mean = (0.3 + 0.7 + 1.2 + … + 20.1)/8 = 4.7 y
Properties of mean and median For symmetric distributions, mean = median For skewed distributions, mean is drawn in direction of longer tail, relative to median Mean valid for interval scales, median for interval or ordinal scales Mean sensitive to “outliers” (median often preferred for highly skewed distributions) When distribution symmetric or mildly skewed or discrete with few values, mean preferred because uses numerical values of observations

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 41

3. Descriptive statistics - 3 Descriptive Statistics...

This preview shows document pages 1 - 12. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online