Imputation. Various problems with data collection can cause some observations to be missing. Suppose a data set has 20 cases. Here are the values of the variable x for 10 of these cases:
17 6 12 14 20 23 9 12 16 21
The values for the other 10 cases are missing. One way to deal with missing data is called imputation. The basic idea is that missing values are replaced, or imputed, with values that are based on an analysis of the data that are not missing. For a data set with a single variable, the usual choice of a value for imputation is the mean of the values that are not missing. The mean for this data set is 15.
(a) Verify that the mean is 15 and find the standard deviation for the 10 cases for which x is not missing.
(b) Create a new data set with 20 cases by setting the values for the 10 missing cases to 15. Compute the mean and standard deviation for this data set.
(c) Summarize what you have learned about the possible effects of this type of imputation on the mean and the standard deviation.