Final answer:
A box plot is an effective tool for showing outliers and skewness of data. It uses the median, quartiles, and whiskers to represent the distribution, making it easy to spot skewness and identify potential outliers.
Step-by-step explanation:
A great tool for showing outliers and skewness of the data is a box plot. A box plot visualizes the distribution of data by depicting the median, quartiles, and potential outliers. To create a box plot, the minimum value, first quartile (Q1), median, third quartile (Q3), and maximum value must be calculated first. After plotting these points, the areas of the plot create a 'box' and 'whiskers'. The 'box' represents the interquartile range (IQR), with the 'whiskers' extending to the smallest and largest values within 1.5 times the IQR from the first and third quartiles, respectively. Values outside of this range are considered potential outliers and are often marked with dots or asterisks.
By examining a box plot, one can quickly assess the symmetry or skewness of the distribution. If the median line within the box is not centered, it indicates skewness. A median closer to the bottom of the box suggests a right skew, while a median closer to the top suggests a left skew. The presence of outliers is easily identifiable as they fall outside the 'whiskers' of the plot.
Histograms are also useful tools for exploring the shape and spread of continuous data. They provide a visual summary of data by showing the frequency of data points within consecutive intervals. Skewness can be observed by the asymmetry in the histogram's shape. However, histograms do not explicitly mark outliers as box plots do. A scatter plot is best when looking at the relationship between two variables, while a bar chart is appropriate for displaying frequencies of categorical data.