Whiskers

Definition

Whiskers, in the context of box plots, are the lines that extend from the box to show the range of the data, excluding outliers. They provide a visual representation of the data's spread and distribution, helping to identify the overall shape and variability of the dataset.

5 Must Know Facts For Your Next Test

1. The length of the whiskers in a box plot is determined by the range of the data, excluding any outliers.
2. Whiskers typically extend to the minimum and maximum values of the data, unless there are outliers present.
3. If there are outliers, the whiskers will only extend to the most extreme non-outlier values, and the outliers will be plotted as individual points.
4. The length of the whiskers provides information about the spread and variability of the data, with longer whiskers indicating a wider range of values.
5. Whiskers can be used to identify the presence and extent of skewness in a dataset, as the relative lengths of the whiskers can indicate the asymmetry of the distribution.

Review Questions

• Explain the purpose and significance of the whiskers in a box plot.
  • The whiskers in a box plot serve to visually represent the range and spread of the data, excluding any outliers. They extend from the box (which represents the first quartile, median, and third quartile) to the minimum and maximum values of the non-outlier data. The length of the whiskers provides information about the variability and distribution of the dataset, with longer whiskers indicating a wider range of values. The relative lengths of the whiskers can also reveal the presence and extent of skewness in the data.
• Describe how the whiskers are affected by the presence of outliers in the dataset.
  • When there are outliers present in the data, the whiskers in the box plot will only extend to the most extreme non-outlier values. The outliers themselves will be plotted as individual points beyond the whiskers. This means that the length of the whiskers no longer represents the full range of the data, but rather the range excluding the outliers. The presence and placement of the outliers can provide important information about the distribution and variability of the dataset, as they indicate observations that fall outside the typical range of the data.
• Analyze how the information conveyed by the whiskers in a box plot can be used to draw conclusions about the underlying data.
  • The whiskers in a box plot offer valuable insights into the shape and distribution of the data. The relative lengths of the whiskers can reveal the degree of skewness in the data, with longer whiskers on one side indicating a skewed distribution. Additionally, the length of the whiskers provides information about the overall spread and variability of the dataset, with longer whiskers suggesting a wider range of values. By examining the whiskers in conjunction with the other elements of the box plot (the box itself and any outliers), researchers can gain a comprehensive understanding of the key characteristics of the data, which can inform statistical analyses, data-driven decision making, and the identification of potential areas for further investigation.

Related terms

Box Plot:

A graphical representation of a dataset that displays the five-number summary: the minimum, first quartile, median, third quartile, and maximum values.

Outlier:

An observation that lies an abnormal distance from other values in a random sample from a population.

Five-Number Summary: A set of five statistics that describe the distribution of a dataset, including the minimum, first quartile, median, third quartile, and maximum values.