wk 3 - measure of dispersion

measures of dispersion

• central tendency

range

the difference between the largest and the smallest observations

• range = max - min

sample variance

• quantifies the amount of variability or spread around the mean of the measurements

  • larger the sample variance = the more dispersed

  • sample variance defined as s²

→ assume that a sample of size n has been randomly drawn from a population, the sample mean is defined as:

xbar= mean

sample standard deviation (s)

• calculated by taking the positive sqaure root

coefficient of variation

• measure of relative variability - defined as the ratio of the standard deviation to the mean multiplied by 100%

• unit free

examples question : sorted dataset

• 2,4,6,7,7

  • mean: 5.2

  • range: 5

  • variance:

  Xbar = 5.2

  • SD:

  • COV:

inter-quartile range

• quartiles divide ordered data into four equal part

boxplots - box and whisker plots

• a useful way of visualizing IQR and outliers

• To generate one, we must find:

  • the 5 point summary (min, Q1, Q2, Q3, max)

  • IQR

  • Upper inside values: the LARGEST value below the upper fence = upper inside value

    → to find upper outer fence Q3 +1.5(IQR)

  • Lower inside values: the smallest value ABOVE the lower fence = lower inside value

    → to find the lower outer fence” Q1 - 1.5 (IQR)