Question 188419
Construct a frequency distribution of the ages that 25 randomly selected smokers started smoking:

26 26 25 17 16 16 14 17 21 16
16 18 17 15 15 19 16 17 22 15
19 17 16 27 16
<pre><font size = 4 color = "indigo"><b>
The smallest number in the list is 14 and the largest is 27 

14 occurs 1 time, so the frequency of 14 is 1
15 occurs 3 times, so the frequency of 15 is 3
16 occurs 7 times, so the frequency of 16 is 7
17 occurs 5 times, so the frequency of 17 is 5
18 occurs 1 time, so the frequency of 18 is 1
19 occurs 2 times, so the frequency of 19 is 2
20 occurs 0 times, so the frequency of 20 is 0
21 occurs 1 time, so the frequency of 21 is 1
22 occurs 1 time, so the frequency of 22 is 1
23 occurs 0 times, so the frequency of 23 is 0
24 occurs 0 times, so the frequency of 24 is 0
25 occurs 1 time, so the frequency of 25 is 1
26 occurs 2 times, so the frequency of 26 is 2
27 occurs 1 time, so the frequency of 27 is 1

We start out with a graph marked
as follows:

{{{drawing(800,400,12,28,-1,8, graph(800,400,12,28,-1,8),
locate(12,7.6,freqency),
line(12.4,0,12.4,7),
line(12.2,1,12.3,1),
line(12.2,2,12.3,2),
line(12.2,3,12.3,3),
line(12.2,4,12.3,4),
line(12.2,5,12.3,5),
line(12.2,6,12.3,6),
line(12.2,7,12.3,7),
locate(12,1.2,1),
locate(12,2.2,2),
locate(12,3.2,3),
locate(12,4.2,4),
locate(12,5.2,5),
locate(12,6.2,6),
locate(12,7.2,7)

 )}}}

Now since 14 occurs 1 time, we draw
a rectangle with height 1, whose base
starts at 13.5 (.5 below 14) and ends
at 14.5 (.5 above 14)

{{{drawing(800,400,12,28,-1,8, graph(800,400,12,28,-1,8),
locate(12,7.6,freqency),
line(12.4,0,12.4,7),
line(12.2,1,12.3,1),
line(12.2,2,12.3,2),
line(12.2,3,12.3,3),
line(12.2,4,12.3,4),
line(12.2,5,12.3,5),
line(12.2,6,12.3,6),
line(12.2,7,12.3,7),
locate(12,1.2,1),
locate(12,2.2,2),
locate(12,3.2,3),
locate(12,4.2,4),
locate(12,5.2,5),
locate(12,6.2,6),
locate(12,7.2,7),
rectangle(13.5,0,14.5,1)
 )}}}

Now since 15 occurs 3 times, we draw
a rectangle with height 3, whose base
starts at 14.5 (.5 below 15) and ends
at 15.5 (.5 above 15)

{{{drawing(800,400,12,28,-1,8, graph(800,400,12,28,-1,8),
locate(12,7.6,freqency),
line(12.4,0,12.4,7),
line(12.2,1,12.3,1),
line(12.2,2,12.3,2),
line(12.2,3,12.3,3),
line(12.2,4,12.3,4),
line(12.2,5,12.3,5),
line(12.2,6,12.3,6),
line(12.2,7,12.3,7),
locate(12,1.2,1),
locate(12,2.2,2),
locate(12,3.2,3),
locate(12,4.2,4),
locate(12,5.2,5),
locate(12,6.2,6),
locate(12,7.2,7),
rectangle(13.5,0,14.5,1), 
rectangle(14.5,0,15.5,3)
 )}}}

Now since 16 occurs 7 times, we draw
a rectangle with height 7, whose base
starts at 15.5 (.5 below 16) and ends
at 16.5 (.5 above 16)

{{{drawing(800,400,12,28,-1,8, graph(800,400,12,28,-1,8),
locate(12,7.6,freqency),
line(12.4,0,12.4,7),
line(12.2,1,12.3,1),
line(12.2,2,12.3,2),
line(12.2,3,12.3,3),
line(12.2,4,12.3,4),
line(12.2,5,12.3,5),
line(12.2,6,12.3,6),
line(12.2,7,12.3,7),
locate(12,1.2,1),
locate(12,2.2,2),
locate(12,3.2,3),
locate(12,4.2,4),
locate(12,5.2,5),
locate(12,6.2,6),
locate(12,7.2,7),
rectangle(13.5,0,14.5,1), 
rectangle(14.5,0,15.5,3),
rectangle(15.5,0,16.5,7)
 )}}}

We continue drawing such rectangles,

{{{drawing(800,400,12,28,-1,8, graph(800,400,12,28,-1,8),
locate(12,7.6,freqency),
line(12.4,0,12.4,7),
line(12.2,1,12.3,1),
line(12.2,2,12.3,2),
line(12.2,3,12.3,3),
line(12.2,4,12.3,4),
line(12.2,5,12.3,5),
line(12.2,6,12.3,6),
line(12.2,7,12.3,7),
locate(12,1.2,1),
locate(12,2.2,2),
locate(12,3.2,3),
locate(12,4.2,4),
locate(12,5.2,5),
locate(12,6.2,6),
locate(12,7.2,7),
rectangle(13.5,0,14.5,1), 
rectangle(14.5,0,15.5,3),
rectangle(15.5,0,16.5,7),
rectangle(16.5,0,17.5,5),
rectangle(17.5,0,18.5,1),
rectangle(18.5,0,19.5,2),
rectangle(19.5,0,20.5,0),
rectangle(20.5,0,21.5,1),
rectangle(21.5,0,22.5,1),
rectangle(22.5,0,23.5,0),
rectangle(23.5,0,24.5,0),
rectangle(24.5,0,25.5,1),
rectangle(25.5,0,26.5,2),
rectangle(26.5,0,27.5,1)
 )}}}

That's all there is to it.

Edwin</pre>