descriptive statistics

statistics of central tendency

• mean (average): arithmetic, harmonic, geometric

• median

• mode

geometric mean

• Nth root of the product of a set of N values

• ex: (2,5,3,4,3), (2×5×3×4×3)^ 1/5 = 3.94

• economics

harmonic mean

• reciprocal of arithmetic mean

• (2,5,3,4,3), 5/(1/2 + 1/5 + 1/3 + ¼ + 1/3) = 3.09

statistics of dispersion

• shows the spread of your data

• range, parametric, sample variance, standard deviation, coefficient of variation

range

difference between the largest and smallest value of a data set

sum of squares

• subtract the mean from the value and square it, add all the resulting values together

• (2,5,3,4,3) (mean: 3.4), (2-3.4)² + (5-3.4)² + (3-3.4)² ……=5.2

parametric variance

sum of squares divided by the number of observations, larger the value the bigger the spread

sample variance

divide sum of squares by (n-1)

standard deviation (SD)

• square root of the variance

• sum of squares → variance → SD

• tells us how much your data deviates from the mean

coefficient of variation (CV)

SD divided by the mean (as a percentage)

Standard error of the mean (SEM)

how accurate your estimate of the mean is likely to be

• divide SD by square root of sample size (n)

• smaller value means more accurate

confidence intervals

Similar to SEM: tells you how accurate your estimate of the mean is

likely to be

• If mean is 7.4 and confidence limits are 5.4 (lower) and 9.4 (upper),

confidence interval is 5.4 to 9.4