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Math Help - Histograms...

  1. #1
    Senior Member Mukilab's Avatar
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    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?
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  2. #2
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    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<br /> <br />
0<t \leq 10 & 20 \\<br />
10<t \leq15 & \text{blank} \\<br />
15 < t \leq 17.5 & 30 \\<br />
17.5 <t \leq20 & 40 \\<br />
20<t\leq25 & \text{blank} \\<br />
25<t \leq40 & \text{blank} \end{array}

    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], 2 units wide.
    The area is 30.
    Hence, the height is: . 30 \div 2\tfrac{1}{2} \,=\,12

    The fourth interval is [17.5, 20], 2 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
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  3. #3
    Senior Member Mukilab's Avatar
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    Quote Originally Posted by Soroban View Post


    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], 2 units wide.
    The area is 30.
    Hence, the height is: . 30 \div 2\tfrac{1}{2} \,=\,12

    The fourth interval is [17.5, 20], 2 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...)
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  4. #4
    Super Member
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    The class intervals can be any amount, but the area in the rectangles is interpreted differently if this is the case.
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