Measures of dispersion

Measures of dispersion

1. tell us how spread or dispersed the data are.

   • indicate the spread or variety of people’s measurements in a distribution.
     • Low dispersion
       • values are similar
     • High dispersion
       • wide range of different values

2. Range

   • highest no/- lowest no
   • use of range is limited, because it tells us nothing about how the data between these two extremes are spread.

3. Percentile

   • divide the data into 100 equal parts with equal numbers of observations in each part.
   • help us to provide information about the location of a score in respect to other scores.
   • score at or below a certain percentage of scores lying in a distribution
   • Quartiles
     • sets of values that divide the distribution into four parts such equal number of observations in each part
     • Q1
       • 25%
         • lower quartile
     • Q2
       • 50%
         • median
     • Q3
       • 75%
         • upper quartile

4. IQR

   • is the companion to the median.
   • indicates the range of values spanned by the middle 50% of the observations
   • Q3-Q1

5. Standard deviation

   • the companion to the mean.
   • indicates the average distance or amount, by which each observation differs from the mean.
     • descriptive statistic that is the most commonly used measure of dispersion or spread
     • denoted by σ, in the population and SD or s in the sample
     • used with the mean to describe the distribution of observations.
       • most widely used measure of dispersion, particularly with interval and ratio level data