Histograms and Frequency Distributions

Basic Understanding of Histograms and Frequency Distributions

  • A Histogram is a graphical representation used to demonstrate the distribution of numerical data.
  • Unlike bar graphs, histograms do not have gaps between the bars, reflecting the continuous nature of the data.
  • The wide bars in a histogram represent the range of data in a particular class.

Frequency Distributions

  • A frequency distribution is a table displaying the frequencies of different categories or classes of data.
  • A frequency distribution table generally consists of two columns: one for the classes of data and the other for their corresponding frequencies.

Constructing a Frequency Distribution Table

  • Identify the range of the data by subtracting the smallest data value from the largest data value.
  • Determine the class width by dividing the range by the desired number of classes. In many cases, this will be between five and twenty.
  • Start the first interval at a value slightly less than the smallest data value and create the remaining intervals by adding the class width successively.
  • Count the number of data points falling within each interval and record this as the frequency for that interval.

Conversion to Histograms

  • The X-axis of a histogram is marked with the boundaries for the class intervals, and the Y-axis is marked with the frequency density.
  • To calculate the frequency density for a class, divide the frequency by the class width.
  • The area under each bar of the histogram (calculated as class width multiplied by frequency density) represents the frequency of data points in that class.

Analysing Histograms

  • Histograms provide valuable insights into the shape of a data distribution and patterns such as skewness, symmetry or bimodality.
  • The bar with the greatest height in the histogram represents the modal class, i.e., the class with the highest frequency of data points.
  • Any noticeable gaps in the histogram indicate classes with no frequency, i.e., ranges where there are no data points.
  • Despite a bar having a small height, its frequency might be high if it corresponds to a wide class interval or range.

Remember that histograms provide a visual representation and do not provide a complete picture of the dataset. They should always be combined with other statistical measures for a comprehensive analysis.