Answer to Question #347793 in Statistics and Probability for Nico

Question

Find (a) the mean, (b) the median, (c) the mode, and (d) the midrange.

Grade Point Averages. The average undergraduate grade point average (GPA) for the 25

top-ranked medical schools is listed below

3.80 3.77 3.70 3.74 3.70

3.86 3.76 3.68 3.67 3.57

3.83 3.70 3.80 3.74 3.67

3.78 3.74 3.73 3.65 3.66

3.75 3.64 3.78 3.73 3.64

Answer 1

Sorted Data Set: 

$$3.57, 3.64, 3.64, 3.65, 3.66,$$

$$3.67, 3.67, 3.68, 3.70, 3.70,$$

$$3.70, 3.73, 3.73, 3.74, 3.74,$$

$$3.74, 3.75, 3.76, 3.77, 3.78,$$

$$3.78, 3.80, 3.80, 3.83, 3.86$$

(a)

$$mean=\dfrac{1}{25}(3.57+ 3.64+3.64+3.65+3.66$$

$$+ 3.67+3.67+3.68+3.70+3.70+3.70$$

$$+3.73+3.73+3.74+3.74+3.74+3.75$$

$$3.76+3.77+3.78+3.78+3.80+3.80$$

$$+3.83+3.86=3.7236$$

(b)

$$median=3.73\ (13^{th} \ place)$$

(c)

$$mode=3.70, 3.74,$$

each appeared 3 times

(d)

$$midrange=\dfrac{3.57+3.86}{2}=3.715$$