# Histograms...

• Jan 11th 2010, 11:24 AM
Mukilab
Histograms...
This will be hard to explain. I understand how histograms work and such but I just don't understand this one
Table:
Time (t seconds): (Frequency beside)
0<t<_10 f=20
10<t<_15 f=blank
15<t<_17.5 f=30
17.5<t<_20 f=40
20<t<_25 f=blank
25<t<_40 f=blank

Complete the histogram. The frequency density is fully blank while the time seconds is partly filled in (missing the 17.5 break).

What I don't understand is how the first one 0<t<_10 f=20 can be 4 boxes high and 10 across (so 4 boxes must be 2). Than 10 to 15 has 16 boxes (so frequency density value of 8) but 5*8 = 40?

This 40 is very confusing because the 15 to 17.5 and 17. to 20 are 30 and 40 accordingly. What have I done wrong?
• Jan 11th 2010, 12:05 PM
Soroban
Hello, Mukilab!

I'm not sure if I understand the problem,
. . but I'll take a guess . . .

Quote:

I understand how histograms work and such but I just don't understand this one.

Table:
$\begin{array}{ccc}\text{Time} & \text{Frequency} \\ \hline

0 10 15 < t \leq 17.5 & 30 \\
17.5 20 25

Complete the histogram.

I see no way to fill in the blanks, so I must assume that "blank" means zero frequency.

The frequency represents an area above the interval.

The first interval is [0,10], ten units wide.
The area is 20.
Hence, the height is 2.

The third interval is [15, 17.5], 2½ units wide.
The area is 30.
Hence, the height is: . $30 \div 2\tfrac{1}{2} \,=\,12$

The fourth interval is [17.5, 20], 2½ units wide.
The area is 40.
Hence, the height is: . $40 \div 2\tfrac{1}{2} \:=\:16$

The histogram looks something like this:
Code:

  |   |                    16   |                    *--*   |                  12|::|   |                *--*::|   |                |::|::|   |                |::|::|   |    2          |::|::|   *-----------*    |::|::|   |:::::::::::|    |::|::|  - + - - + - - + - - + -+- + - - + - - + - - + - - + - -   0    5    10    15    20    25    30    35    40
• Jan 11th 2010, 12:09 PM
Mukilab
Quote:

Originally Posted by Soroban

The frequency represents an area above the interval.

The first interval is [0,10], ten units wide.
The area is 20.
Hence, the height is 2.

The third interval is [15, 17.5], 2½ units wide.
The area is 30.
Hence, the height is: . $30 \div 2\tfrac{1}{2} \,=\,12$

The fourth interval is [17.5, 20], 2½ units wide.
The area is 40.
Hence, the height is: . $40 \div 2\tfrac{1}{2} \:=\:16$

[/code]

You have a graph which supplements the blanks.

Sorry, my actual question without the rambling is: Can the frequency be any amount? Or does it have to go in an orderly manner such as <t<_20 then <t<_30 then <t<_40

And I guess I was just freaked out by their plotting of frequency density (was in 4s...)
• Jan 11th 2010, 06:09 PM
ANDS!
The class intervals can be any amount, but the area in the rectangles is interpreted differently if this is the case.