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Diagrams

In elementary school, various types of diagrams are used in statistics to help visualize and understand data. Some of the most common diagrams include:

Bar/Column Chart

Often, many names are used for a diagram like this. Some call it a bar chart, while others call it a column chart. There is no definitive definition of what constitutes a bar, column, or stick diagram. However, note that under each "stick," there is only one value.

  • For the bar chart, the column h(x) or f(x) is used as the series value, and shoe size is used as the category.

 

Pie Chart

Box Plot

A box plot shows the minimum value, 1st quartile, median, 3rd quartile, maximum value, and range.


Shows the distribution of shoe sizes for boys and girls.

From the box plot, one can see for the boys:

  • The middle 50% have a shoe size between 41 and 44 (both included).
  • The first 25% have a shoe size between 36 and 41 (both included).
  • The last 25% have a shoe size between 44 and 47 (both included).
  • 25% have a maximum shoe size of 41.
  • 75% have a minimum shoe size of 41.
  • 75% have a maximum shoe size of 44.
  • The last 25% have a shoe size of 44 or greater.
  • The difference in shoe size among the first 25% of observations is greater than the last 25%.

 

Cumulative Frequency Curves

A cumulative frequency curve, or cumulative frequency graph, displays how many observations in a dataset lie below a certain value. For example, it can show how many students in a class are shorter than a specific height.

When analyzing a cumulative frequency curve, one can also identify the quartiles. The quartiles divide the dataset into four equal parts: the lower quartile (25%), the median (50%), and the upper quartile (75%). These points on the curve help us understand how the data is distributed and where most observations lie. By examining the quartiles in a cumulative frequency curve, we can quickly assess whether the data is evenly distributed or concentrated around specific values.

To create a cumulative frequency curve, it's best to use the cumulative frequency F(x) as a starting point, but the cumulative frequency count H(x) can also be used.