Answer for Review Exercise 6.

Note: V, ^ <, and > represent down, up, left, and right arrows,
respectively.

Histogram and median calculation for Problem 4(a).
The percentages inside the recangles is the percentage of observations
in that bin.  The percentages outside the rectangles are the cumulative
percentages known as percentiles.

Use interpolation to to find the median x within the third rectangle.

Histogram (a)
                            50%                      Solve for the median x:
                             |                       50 - 40     x - 2
                        40%  V     90%               -------  =  -----
50 +                     +---------+                 90 - 40     3 - 2
   |                     |         |
40 +                     |         |                 10 / 50 = (x - 2) / 1
   |          10%        |         | 
30 +           +---------+         |                 0.2 = x - 1
   |           |         |    50%  |
20 +           |         |         |                 median = x = 1.2
   | 0%        |    30%  |         |        100%
10 + +---------+         |         +---------+
   | |   10%   |         |         |   10%   |
 0 + +---------+---------+---------+---------+
    0          1         2  ^      3         4
                            |
                            x

Histogram (b)  The percentage of observations in the third rectangle is 20%,
               which is the area of the rectangle. The width of this rectangle
               is 2, so is height must be area / base 10% per horizontal unit. 
               
                  50%
                   |
              30%  V    80%                          50 - 30   x - 1
50 +           +---------+                           ------- = -----
   |           |         |                           80 - 30   2 - 1
40 +           |         |
   | 0%        |         |                           20 / 50 = (x - 1) / 1
30 + +---------+         |
   | |         |    50%  |                           0.4 = x - 1
20 + |         |         |
   | |   30%   |         |                  100%     median = x = 1.4
10 + |         |         +-------------------+
   | |         |         |        20%        |
 0 + +---------+---------+---------+---------+
     0         1   ^     2         3         4
                   |
                   x

Histogram (c)  The percentage of observations in the third rectangle is 30%.
               Height = 30 / (2.5 - 2) = 60
               Height of fourth rectangle is 10 / (3 - 2.5) = 20.
               
                        60%  90%
60 +                     +----+             50 - 20   x - 1
   |                50%  |    |             ------- = -----
50 +                 |   |    |             60 - 20   2 - 1
   |          20%    V   |    |
40 +           +---------+    |             30 / 40 = (x - 1) / 1
   |           |         |    |
30 +           |         |30% |             0.75 = x - 1
   | 0%        |         |    |   100%
20 + +---------+   40%   |    +----+        median = 1.75
   | |         |         |    |    |
10 + |   20%   |         |    |10% |
   | |         |         |    |    |
 0 + +---------+---------+----+----+
     0         1     ^   2         3         
                     |
                     x