Question

A recent report indicated that, “On average (mean), adolescents begin experimenting with drugs at the age of 13 years.” This information is used to determine which grade level to begin a drug abuse resistance program, similar to the DARE program. Consistent with this finding the police department you work for decides to implement the drug abuse resistance program for 13 year old children, or in the eighth grade.

You believe, based on your experience as a school resource officer in the elementary schools, that this is too old and that the program should be started earlier. Specifically, your experience teaches you that pressure to experiment with drugs appears to start in the sixth grade, or about 11 years old.

As you prepare to meet with the chief of police you again review the report. In it you find that the mean average age of onset is 13, but that the median age of onset is 11. Based solely on what you have learned about the meaning, advantages and disadvantages of the three measures of central tendency (mean, median and mode) develop a recommendation to begin the drug abuse resistance program during the sixth grade. In other words, present an argument that in this case the median is a more reliable measure of central tendency than the mean.

Answer 1

To answer this question let's start with the definitions. So It will be easy to explain the importance of median over mean and mode in this question.
Definitions:

Mean: The mean is equal to the sum of all the values in the data set divided by the number of values in the data set.
Median: The median is the middle value for a set of data that has been arranged in order of magnitude.
Mode: The mode is the most frequent value in our data set.

From the definition, it is clear that the mean depends on all the values present in the data set. If we change any of the value then the result will be affected. Mean is particularly susceptible to the influence of outliers. These are values that are unusual compared to the rest of the data set by being especially small or large in numerical value. So, the mean doesn’t always locate the center of the data accurately.

In mode, if the value will not repeat then there will be no mode in data. But, If you take the date of birth of the children then very there is a very high chance that the number will repeat. It is a very high chance that the central tendency will give an inaccurate result.

Unlike the mean, the median value doesn’t depend on all the values in the dataset. Consequently, when some of the values are more extreme, the effect on the median is smaller. It is just the middle value of the data set. The median is less affected by outliers and skewed data.

Now in our case, the median is the best central tendency to implement the drug abuse resistance program for 11-year-old children. The mean is highly affected by the outliers( as any child age is extremely high or low). And it is also better for children to aware of Drug abuse at 11 years old age rather than 13-year-old age. so in this case "in this case the median is a more reliable measure of central tendency than the mean"