Word Problem

Question

The five-number summary for midterm scores {number of points; the maximum possible score was 50 points} from an intro stats class is : Min 16.5, Q1 32, Median 39, Q3 43.5, Max 48.5. Would you expect the mean midterm score of all students who took the midterm to be higher or lower than the median? Explain.

Answer 1

The problem statement divides  the scores into four groups (with approximately 25% of the scores in each group):

 

               25%                 25%                  25%                    25%

    |                        |                       |                        |                        |

  16.5                   32                     39                     43.5                   48.5

 

The mean is the arithmetic average.  it Is impacted by "outliers."

 

Since we know nothing (mean, median, or mode) regarding the distribution of scores in each of the four ranges given, a very simple tactic is to take the average (mean) of the four mid-range values:

     (24.35 + 35.5 + 41.25 + 46)/4 = 36.75

 

I would expect the mean to be be lower than the median.