Cumulative frequency curves

Introduction to Cumulative Frequency Curves

  • A Cumulative Frequency Curve, also known as an ‘Ogive’, is commonly used in statistics to provide a visual representation of data.
  • It plots cumulative frequency against the upper class boundary, assisting to comprehend the distribution of data values.
  • It gives a running total of the data as you move along the axis.

Constructing a Cumulative Frequency Curve

  • To construct a Cumulative Frequency Curve, you will first need the upper class boundaries and their corresponding cumulative frequencies.
  • Plot these points on a graph, with the upper class boundaries on the x-axis and cumulative frequencies on the y-axis.
  • Plot each point (upper class boundary, cumulative frequency) and join the points with a smooth curve from left to right.
  • The curve should start at zero and end at the total frequency, giving a complete overview of the data distribution.

Interpreting a Cumulative Frequency Curve

  • A Cumulative Frequency Curve is used to make estimates and predictions about your data.
  • It helps to identify the median, lower quartile, upper quartile, and can also be used to estimate the inter-quartile range (IQR).
  • The median is found at the point that corresponds to half the total frequency on the y-axis.
  • The lower quartile (Q1) is found at the point that corresponds to a quarter of the total frequency and the upper quartile (Q3) is found at the point that corresponds to three quarters of the total frequency on the y-axis. Inter-quartile range (IQR) is calculated by Q3 - Q1.
  • It’s important to note that these values are estimated and may not perfectly represent the data set.

Revision Tips

  • Familiarise yourself with the concept of cumulative frequency curves, why they are used, and what they represent.
  • Regular practice in drawing cumulative frequency graphs will help understand this topic better.
  • Make sure you understand how to read the range, median, quartiles, and interquartile range from a cumulative frequency curve.
  • Do not forget to revisit the formula for IQR and the importance of identifying outliers in a data set.
  • Use plenty of practice problems to reinforce your understanding of these concepts.