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Histograms???????
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Hi I have a table showing Time(t) in minutes with info below, then Frequency but no info below. How am I supposed to work out the frequency on the info i have?
Answers
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You've got me confused!
I think (but I'm not sure) that you mean that you've got a (complete) histogram from which you're asked to transfer data to a (currently incomplete) table. If so, it would help to know the labels on the horizontal and vertical axes. (I'm guessing that these are 'time' and 'frequency density').
The important thing to remember about a histogram (which makes it different from a simple bar chart) is that it's the AREA of each 'bar' (rather than it's height) which represents the frequency. For example if the first 'bar' goes across from 0 minutes to 10 minutes and it's height is shown as '5' then, when you come to complete the table, the frequency alongside '0-10' minutes will be 50 (i.e. 10 x 5).
Does that help?
Chris
I think (but I'm not sure) that you mean that you've got a (complete) histogram from which you're asked to transfer data to a (currently incomplete) table. If so, it would help to know the labels on the horizontal and vertical axes. (I'm guessing that these are 'time' and 'frequency density').
The important thing to remember about a histogram (which makes it different from a simple bar chart) is that it's the AREA of each 'bar' (rather than it's height) which represents the frequency. For example if the first 'bar' goes across from 0 minutes to 10 minutes and it's height is shown as '5' then, when you come to complete the table, the frequency alongside '0-10' minutes will be 50 (i.e. 10 x 5).
Does that help?
Chris
Hi the complete info i have is as follows:
Q. The table gives information about how long in minutes,
students took to complete a puzzle.
The Table:
Time (t) in minutes Frequency
0 < t (> with - under it) 1020
10< t (> with - under it) 1530
15 <t (> with - under it) 3060
30 < t (> with - under it) 6090
Use the table to draw a histogram.
The graph to place it on has nothing on the vertical, on horizontal 0 - 60 (in tens) underneath Time (t) in minutes.
Hope this is clear enough as i do not understand it at all to be able to describe it any better. Thank you if you can help.
Q. The table gives information about how long in minutes,
students took to complete a puzzle.
The Table:
Time (t) in minutes Frequency
0 < t (> with - under it) 1020
10< t (> with - under it) 1530
15 <t (> with - under it) 3060
30 < t (> with - under it) 6090
Use the table to draw a histogram.
The graph to place it on has nothing on the vertical, on horizontal 0 - 60 (in tens) underneath Time (t) in minutes.
Hope this is clear enough as i do not understand it at all to be able to describe it any better. Thank you if you can help.
(2-part post):
OK. I think I understandwhat you've got.
The first interval is 0<t<10, with a frequency of 20. So, what it means is that 20 students took between 0 and 10 minutes to complete the puzzle. (The extra line under the second < sign simply means that anyone who took exactly 10 minutes is included in this group, rather than in the next one).
Your first bar on the histogram has to represent this information but, as I stated before, it has to be the AREA of the bar (and not it's height) which matches the frequency. The bar extends across from 0 seconds to 10 seconds so, obviously, its width is 10. Therefore, in order for it to have an area of 20, its height should be 2.
The second interval is 10<t<15, with a frequency of 30. This means that 30 students took between 10 and 15 minutes to complete the puzzle. When you represent it on the histogram, the bar will extend across from 10 to 15 (so its width is 5). But the area must match the frequency (30). This dictates that its height must be 6.
The third interval is 15<t<30, with a frequency of 60. So, 60 students took between 15 and 30 minutes to do the puzzle. When you draw the bar, it will go across from 15 to 30, so its width is 15. In order for the area to match the frequency (60), its height must be 4.
The final interval is 30<t<60, with a frequency of 90. (i.e. 90 students took between 30 and 60 minutes to complete the puzzle). The bar on the histogram goes across from 30 to 60, so its width is 30. But the area must be 90 which means that the height must be 3.
OK. I think I understandwhat you've got.
The first interval is 0<t<10, with a frequency of 20. So, what it means is that 20 students took between 0 and 10 minutes to complete the puzzle. (The extra line under the second < sign simply means that anyone who took exactly 10 minutes is included in this group, rather than in the next one).
Your first bar on the histogram has to represent this information but, as I stated before, it has to be the AREA of the bar (and not it's height) which matches the frequency. The bar extends across from 0 seconds to 10 seconds so, obviously, its width is 10. Therefore, in order for it to have an area of 20, its height should be 2.
The second interval is 10<t<15, with a frequency of 30. This means that 30 students took between 10 and 15 minutes to complete the puzzle. When you represent it on the histogram, the bar will extend across from 10 to 15 (so its width is 5). But the area must match the frequency (30). This dictates that its height must be 6.
The third interval is 15<t<30, with a frequency of 60. So, 60 students took between 15 and 30 minutes to do the puzzle. When you draw the bar, it will go across from 15 to 30, so its width is 15. In order for the area to match the frequency (60), its height must be 4.
The final interval is 30<t<60, with a frequency of 90. (i.e. 90 students took between 30 and 60 minutes to complete the puzzle). The bar on the histogram goes across from 30 to 60, so its width is 30. But the area must be 90 which means that the height must be 3.
Draw the histogram as I've indicated (choosing a suitable scale so that the vertical axis goes up to 6). The vertical axis should be labelled 'frequency density'.
The key points to remember (so that you'll be able to get future questions right) are these:
1. Whenever you see a pair of 'less than' symbols, you should read this as 'lies in between'. (So 6.2<x<8.1 is simply read as 'x lies in between 6.2 and 8.1'. If, in that example, x could actually be equal to 6.2, the first < sign would have an extra line underneath to include the 'equals' bit. A similar line under the second < sign would mean that x could actually be equal to 8.1).
[By the way, if the question you've been given really does state 0<t>10, 10<t>15, etc, (which is what you've said) the person who wrote it should be shot! It's meaningless!].
2. As I've said twice before, the important thing to remember about histograms is that its the areas (and not the heights) of the bars which represent the frequencies.
Chris
The key points to remember (so that you'll be able to get future questions right) are these:
1. Whenever you see a pair of 'less than' symbols, you should read this as 'lies in between'. (So 6.2<x<8.1 is simply read as 'x lies in between 6.2 and 8.1'. If, in that example, x could actually be equal to 6.2, the first < sign would have an extra line underneath to include the 'equals' bit. A similar line under the second < sign would mean that x could actually be equal to 8.1).
[By the way, if the question you've been given really does state 0<t>10, 10<t>15, etc, (which is what you've said) the person who wrote it should be shot! It's meaningless!].
2. As I've said twice before, the important thing to remember about histograms is that its the areas (and not the heights) of the bars which represent the frequencies.
Chris
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