1. Descriptive Statistics – Graphic Guidelines
Pie charts – qualitative variables, nominal data, eg. ‘religion’
Bar charts – qualitative or quantitative variables, nominal or interval data, eg. ‘religion’ or ‘margin debt’; time series or cross sectional data
Line graphs – quantitative variables, interval data, eg. margin debt; time series data
Histograms – quantitative variables, interval data, eg. golf scores; cross sectional data – depicts the SHAPE of a frequency distribution
Stem and Leaf Plot– quick and dirty histogram
Ogive – depicts a cumulative frequency distribution
Scattergram – two quantitative variables, eg. Margin vs, the market value

2. Descriptive Statistics –
Numeric Measures
CENTER
Mean
Median
Mode
Mid-point of the range
SPREAD (dispersion)
Standard deviation
Variance
Range
Quartiles
Interquartile range
Percentiles

3. Z Scores and t-scores
Measures distance from the mean in standard deviations
Eg. T score for bone density – 1 to 2.5 standard deviations below the norm (mean) for a 23 year old indicates osteopenia; 2.5 or more indicates osteoporosis
(X-m)/s = z score
(X – Xbar)/s = t score

4. Empirical Rule For mound shaped distributions
About 68% of observations are within one standard deviation of the mean
About 95% of observations are within two standard deviations of the mean
Almost all observations are within three standard deviations of the mean

5. Chebyshev’s Rule For all distributions
Let k be greater than or equal to 1
At least 1-(1/k2) of the observations are within k standard deviations of the mean
Examples
K=1 zero observations may be within one standard deviation of the mean
K=2 3/4th’s of observations must be within two standard deviations of the mean
K=3 8/9th’s of observations must be within three standard deviations of the mean

6. Objectives for BUSA 5325: Advanced Statistical Methods
To define histogram, mean, median, mode, range, skewness, standard deviation, variance, z-score
To discuss conditions under which the mean is preferred to the median as a measure of central tendency.
To describe the shape, center, and dispersion of a data set verbally, graphically, and/or numerically including construction and use a histogram, box plot, and a cumulative relative frequency line chart (i.e., ogive)