Smoothed Histograms

Cumulative Frequency Graphs

• Ogives provide a smoothed representation of cumulative frequencies.

Key Terms

• Frequency refers to the number of observations or occurrences in each category.

Ogive Characteristics

• In ogives, line segments connecting midpoints form a cumulative frequency curve.
• The overall direction or shape of the line in an ogive is described as monotonic.

Graph Axes

• Axes in a graph typically represent the variables being measured, such as frequency and category.

Ogive Interpretation

• An S-shaped curve formed by connecting cumulative frequencies represents the distribution of data.
• The primary purpose of an ogive is to display the cumulative frequency of a distribution.
• Ogives are applicable to discrete or continuous data.

Advantages and Disadvantages

• An advantage of using ogives over histograms is that ogives provide a clearer picture of the cumulative frequency.
• Interpreting ogives can be challenging for less experienced readers due to the cumulative nature of the data.

Other Graph Types

• A graph specifically designed for visualizing the distribution of continuous data is an ogive.
• A histogram assumes equal widths of the bars, and this assumption can influence the appearance of the histogram.
• The primary purpose of a histogram is to display the distribution of data.
• Continuous data is most suitable for representation using a frequency polygon.
• The width of the bars in a histogram represents the class interval or bin width.
• A frequency polygon is different from a histogram in that it is a line graph, whereas a histogram is a bar graph.
• Bin width is a key term associated with the choice that can influence the appearance of a histogram.
• A common disadvantage of histograms and frequency polygons is that they can be misleading if the bin width or class interval is not chosen carefully.