Use the mean to describe the sample with a single value that represents the center of the data. Many statistical analyses use the mean as a standard measure of the center of the distribution of the data.
The median is another measure of the center of the distribution of the data. The median is usually less influenced by outliers than the mean. Half the data values are greater than the median value, and half the data values are less than the median value.
The median and the mean both measure central tendency. But unusual values, called outliers, can affect the median less than they affect the mean. If your data are symmetric, the mean and median are similar.
Step 2: Determine a confidence interval for the mean, median, and standard deviation
The confidence interval provides a range of likely values for the population parameter. For example, a 95% confidence level indicates that if you take 100 random samples from the population, you could expect approximately 95 of the samples to produce intervals that contain the population parameter.
Step 3: Assess the shape and spread of your data distribution
Use the histogram and boxplot to assess the shape and spread of the data, and to identify any potential outliers.
Examine the spread of your data to determine whether your data appear to be skewed
When data are skewed, the majority of the data are located on the high or low side of the graph. Often, skewness is easiest to detect with a histogram or boxplot.
Outliers, which are data values that are far away from other data values, can strongly affect the results of your analysis. Often, outliers are easiest to identify on a boxplot.
Try to identify the cause of any outliers. Correct any data–entry errors or measurement errors. Consider removing data values for abnormal, one-time events (also called special causes). Then, repeat the analysis. For more information, go to Identifying outliers.
Look for multi-modal data
Multi-modal data have multiple peaks, also called modes. Multi-modal data often indicate that important variables are not yet accounted for.
If you have additional information that allows you to classify the observations into groups, you can create a group variable with this information. Then, you can create the graph with groups to determine whether the group variable accounts for the peaks in the data.