Question

Which measures of central tendency should be reported for each of the following examples? Explain your reasoning.

·        A dress manufacturer wants to know the average dress size of women.

·        A researcher wants to separate people on the basis of a personality tests into two groups of equal sizes: a high-anxiety group and a low-anxiety group.

·        Students rated a professor as an effective instructor using a scale of 1 to 5 with 1 meaning strongly agree and 5 meaning strongly disagree.

·        In a timed problem-solving experiment, some of the participants failed to solve the problem within a reasonable period of time. The experimenter would like to include these participants in his measure of average time to solve the problem.

Answer 1

   A dress manufacturer wants to know the average dress size of women.

Here, the best average would be Mode. As the modal value will fit to most of the women as compared to median or mean value and will not accumulate outliers.

A researcher wants to separate people on the basis of a personality tests into two groups of equal sizes: a high-anxiety group and a low-anxiety group.

Here, the best average would be Median. As the data needs to be divided in two equal parts and median does this the best as it is the center of the data set.

Students rated a professor as an effective instructor using a scale of 1 to 5 with 1 meaning strongly agree and 5 meaning strongly disagree.

Here, the best average would be Median. As the data is ordinal and median is the best representative of ordinal data set

In a timed problem-solving experiment, some of the participants failed to solve the problem within a reasonable period of time. The experimenter would like to include these participants in his measure of average time to solve the problem.

Here, the best average would be Mean. Because here the outliers are needs to be included and mean is the central tendency which gives weight to all the values including outliers.