Quartiles Percentiles

Contents

  • Cumulative Frequency Graph
  • Quartiles & Inter-quartile Range
  • Box and Whisker Plots
  • Finding Quartiles
  • Finding Percentiles

Cumulative Frequency Graph

Cumulative frequency graph is drawn using values in x axis and cumulative frequencies in y axis.

Quartiles & Inter-quartile Range

Quartiles divide the total frequency into 4 equal parts.

Quartiles are denoted by

Q1 – First or Lower Quartile.

Q2 – Second Quartile or Median.

Q3 – Third or Upper Quartile.


Inter Quartile Range = Q3 – Q1

Box-and-Whisker Plot

Box and whisker plot is drawn using lowest value, highest value and three quartiles.

Box is drawn using three quartiles.

Lines are drawn from either side of the box to the lowest value and highest value.

Finding Quartiles

Σf/4 = 120/4 = 30

Draw a horizontal line from 30 to touch the graph.

Draw a vertical line from this point to meet the X axis at the First Quartile, Q1.

Similarly find Q2 and Q3.

Finding Percentiles

Percentiles divides the total frequency into 100 equal parts.

Percentiles are denoted by

P1, P2, P3,…,P99.

P50 – 50th Percentile is the Median.

50Σf/100

= 50x120/100 = 60.

Draw a horizontal line from 60 to touch the graph.

Draw a vertical line from this point to meet the X axis at the 50th percentile, P50.