Depending on how a data set is distributed, its histogram can take on different shapes. There are two main types.
If the data is distributed somewhat evenly around the mean, the bars on each side of the middle bar will have roughly the same height. This is called a symmetric distribution.
In a symmetric histogram, the mean is typically found in the tallest bar.
When the data is not evenly distributed around the mean the histogram becomes skewed.
For skewed histograms, the mean is usually not found in the tallest bar.
Based on the distribution of a data set, different types of statistics are more suitable than others.
For a symmetric distribution, all values are spread out somewhat evenly around the center. Since both the mean and standard deviation take into account the actual values of all data points, these statistics are usually more suitable when describing this distribution.
Two ketchup companies investigate the weight of their -ounce bottles. Below are the results for both companies.
Analyze the results for both companies and determine which statistics are more suitable.
The general shape of the first histogram is symmetric, since the bars on opposite sides of the middle bar are roughly the same height. Therefore, Red Queen should use the mean and standard deviation to describe the results of their survey. The results for Red Rising are, however, skewed to the right. Therefore, they should use the median and interquartile range.
Since the histogram for Red Queen is symmetric, we can assume they fill their bottles more evenly than Red Rising. However, the amount of ketchup in each bottle is more for Red Rising. Red Rising should probably consider adopting more consistent practices.