Question

Consider a random sample of 5 individuals (n = 5).  Let ?i be the final grade earned in a particular professor’s class on a 4‐point GPA scale, where 4 = A, 3 = B, 2 = C, 1 = D, and 0 = F. Using an equation editor, compute the arithmetic mean, geometric mean, median, and mode “by hand.”

Using an equation editor, compute the range, variance, standard
deviation, coefficient of variation, and interquartile range “by hand.”
C. Using an equation editor, compute kurtosis and excess kurtosis “by
hand.” Is this distribution mesokurtic, leptokurtic, or platykurtic?
Intuitively explain.

Answer 1

Mean=(4+3+2+1+0)/5=2.

Since F=0, we can't compute geometric mean.

Median:

We arrange the data in increasing order: 0, 1, 2, 3, 4.

Median=(5+1)/2 i.e. 3rd observation=2.

Mode does not exist since all observations appear exactly once.

Range=4-0=4.