Question 345162
<pre>
I'll choose 6 classes.

Maximum = 52
Minimum = 15
{{{(Maximum - Minimum)/6 = 37/6 = 6.1666667}}}
Always round up to the next higher integer, 
never round down.  So we round up to 7

So width of each class is 7.  We start {{{1/2}}} a unit
before the smallest value or 6.5, then we add 7 and get 
13.5.  So we begin with the first class:

   CLASS
14.5 -- 21.5 

Then we start the next class at the same value the previous
class ended, 21.5, and add 7 again and get 27.5.  So the 
second class is from 21.5 to 27.5 and we write it below the
first class: 

    CLASS
14.5 -- 21.5
21.5 -- 28.5

And we continue the same way through the 6 classes, and we end
up with this

    CLASS
14.5 -- 21.5     
21.5 -- 28.5
28.5 -- 35.5
35.5 -- 42.5
42.5 -- 49.5
49.5 -- 56.5

Now we count the number of numbers in each class, and make a column
of frequencies (the number of numbers in each class).  As a check to
see that you counted correctly, always add the column of frequencies
to make sure you get the the total number of numbers, which is 40

    CLASS        FREQUENCY
14.5 -- 21.5        2
21.5 -- 28.5        4
28.5 -- 35.5       17
35.5 -- 42.5       13
42.5 -- 49.5        2
49.5 -- 56.5        2
---------------------------
       TOTAL       40


To make the histogram, we start off with an x-axis marked
off with the class bounds, and a y-axis, not joined to
the x-axis as in regular algebra, but just sitting off to the
left side marked off with numbers from 0 going up to the highest 
frequency (or more).

{{{drawing(600,400,-2,7,-1,18,

line(0,0,6,0), 
line(0,0,0,.3),line(1,0,1,.3),line(2,0,2,.3),line(3,0,3,.3),line(4,0,4,.3),line(5,0,5,.3),line(6,0,6,.3),

locate(0-.25,0,14.5),locate(1-.25,0,21.5),locate(2-.25,0,28.5),locate(3-.25,0,35.5),locate(4-.25,0,42.5),locate(5-.25,0,49.5),locate(6-.25,0,56.5),

line(-.6,0,-.6,18),
line(-.7,0,-.5,0),line(-.7,1,-.5,1),line(-.7,2,-.5,2),line(-.7,3,-.5,3),
line(-.7,4,-.5,4),line(-.7,5,-.5,5),line(-.7,6,-.5,6),line(-.7,7,-.5,7),
line(-.7,8,-.5,8),line(-.7,9,-.5,9),line(-.7,10,-.5,10),line(-.7,11,-.5,11),
line(-.7,12,-.5,12),line(-.7,13,-.5,13),line(-.7,14,-.5,14),line(-.7,15,-.5,15),
line(-.7,16,-.5,16),line(-.7,17,-.5,17),

locate(-1,.42,0),locate(-1,1.42,1),locate(-1,2.42,2),locate(-1,3.42,3),
locate(-1,4.42,4),locate(-1,5.42,5),locate(-1,6.42,6),locate(-1,7.42,7),
locate(-1,8.42,8),locate(-1,9.42,9),locate(-1.1,10.42,10),locate(-1.1,11.42,11),
locate(-1.1,12.42,12),locate(-1.1,13.42,13),locate(-1.1,14.42,14),locate(-1.1,15.42,15),
locate(-1,16.42,16),locate(-1,17.42,17)


  )}}}

Next we draw 6 join rectangles, each one as high as
the frequency of the class whose boundary is at its
bottom left and bottom right corner.




{{{drawing(600,400,-2,7,-1,18,

line(0,0,6,0), 
line(0,0,0,.3),line(1,0,1,.3),line(2,0,2,.3),line(3,0,3,.3),line(4,0,4,.3),line(5,0,5,.3),line(6,0,6,.3),

locate(0-.25,0,14.5),locate(1-.25,0,21.5),locate(2-.25,0,28.5),locate(3-.25,0,35.5),locate(4-.25,0,42.5),locate(5-.25,0,49.5),locate(6-.25,0,56.5),

line(-.6,0,-.6,18),
line(-.7,0,-.5,0),line(-.7,1,-.5,1),line(-.7,2,-.5,2),line(-.7,3,-.5,3),
line(-.7,4,-.5,4),line(-.7,5,-.5,5),line(-.7,6,-.5,6),line(-.7,7,-.5,7),
line(-.7,8,-.5,8),line(-.7,9,-.5,9),line(-.7,10,-.5,10),line(-.7,11,-.5,11),
line(-.7,12,-.5,12),line(-.7,13,-.5,13),line(-.7,14,-.5,14),line(-.7,15,-.5,15),
line(-.7,16,-.5,16),line(-.7,17,-.5,17),

locate(-1,.42,0),locate(-1,1.42,1),locate(-1,2.42,2),locate(-1,3.42,3),
locate(-1,4.42,4),locate(-1,5.42,5),locate(-1,6.42,6),locate(-1,7.42,7),
locate(-1,8.42,8),locate(-1,9.42,9),locate(-1.1,10.42,10),locate(-1.1,11.42,11),
locate(-1.1,12.42,12),locate(-1.1,13.42,13),locate(-1.1,14.42,14),locate(-1.1,15.42,15),
locate(-1,16.42,16),locate(-1,17.42,17),


line(0,0,6,0), 
rectangle(0,0,1,2),
rectangle(1,0,2,4),
rectangle(2,0,3,17),
rectangle(3,0,4,13),
rectangle(4,0,5,2),
rectangle(5,0,6,2)  )}}} 

That's the histogram.  It is mound shape (or "bell"-shaped) because
it bulges up in the middle.

Edwin</pre>