Representation of Data - Measures of Dispersion

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Types of Dispertion measures

Range - The sum of the large value subtract the small value

Quartiles - Divide the data into 4 equal parts

  • 25% of the observations are less or equal to the first quartile (Q1)
  • 50 % of the observations are less than or equal to the second quartile (Q2, Median)
  • 75% of the observations are less than or equal to the third quartile (Q3)

Interquartile Range - The value obtained when Q3 - Q1

Semi Interquartile Range - Half of the interquartile range

Percentiles - Divide the data into 100 equal parts

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Representation of Data

Outliers - an extreme value that does not fit the body of the data

Histogram - used to represent a continuous variable that has been summarised by a group frequency distribution. Frequency density = Frequency/Class width

Relative Frequency - A frequency expressed as a proportion of the total frequency

Box Plot - A diagram that shows the smallest value, Q1, median, Q3 and largest value

Skewness - Skewness is an indicator of the shape of distribution

  • Symmetrical - Q2 - Q1 = Q3 - Q2
  • Positive Skew - Q2 - Q1 < Q3 - Q2
  • Negative Skew Q2 - Q1 > Q3 - Q2
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