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

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

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

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

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

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)