What statistics and graphs can you use to answer the following question: Is the distribution ...

Ans. #1

A histogram can show you whether a distribution is symmetric, positively skewed, negatively skewed, or has a different shape. If the data is symmetric, a histogram can tell you whether the data is bell shaped, bimodal, or uniform, etc. A box plot can also show you whether a distribution is symmetric, negatively skewed or positively skewed. However, it can't tell you what the exact shape is, if the data are found to be symmetric. For example, a box plot cannot tell you whether a symmetric data set is unimodal or bimodal. This is a drawback of a box plot.

Ans. #2

A histogram can show you the number of modes of a distribution, as well as where they are located. A box plot cannot tell you where any of the modes of a distribution are, or even how many might exist. It just shows you distances between certain milestones in the distribution, such as the five-number summary. This is a drawback of a box plot.

Ans. #3

The standard deviation can tell you whether the observations are close to or spread out from the middle. The interquartile range tells how far apart them middle 50 of the data are, and works especially well for skewed data. A histogram and a box plot can show you how close together/spread out the data appear visually.

Ans. #4

The median is a better measure of center for skewed data, and the mean works well for symmetric data. If the data is skewed, a box plot can show you where the median is. If the data is symmetric, a histogram can give you an idea where the mean is.

Ans. #5

shape

Ans. #6

Graphical; numerical

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