1. ## 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?

2. Hello, Mukilab!

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

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

3. 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...)

4. The class intervals can be any amount, but the area in the rectangles is interpreted differently if this is the case.