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Firstly, what *is* relative frequency please?
Secondly, given this, could you tell me the answer to the following query:
"Graham tosses matchsticks onto a 2cm grid. He records the number of lines each matchstick crosses.
Here's his results:
No. of lines crossed ¦ Frequency
0 0
1 2
2 14
3 21
4 3
a) Work out the relative frequency for each number of lines crossed. Write them in decimals. Check they add up to 1.
b) If the matchstick were dropped 250 times, how many times would it cross two lines?
The Relative frequency of a situation (i.e. 1 line crossed) is the amount of times that situation occurs (its frequency) in relation to everything else.
I.e. in your example, the frequency of "1 line crossed" is 2, but the Relative frequency is 2/40 (as there were 40 tosses overall.
They add up to one because, the relative frequency of getting any result is always 1. (You have to get some result)
Table:
# lines___Freq___Rel. Freq
__0_______0_______0___
__1_______2_______0.05_
__2_______14______0.35_
__3_______21______0.525
__4_______3_______0.075
__Total____40______1.000
The number of times it *should* cross two lines, based on this data, after 250 thows, is 250 * relative freq. of "2 lines crossed"
= 250 * 0.35 = 87.5
As you can't have half a time, it would have to be rounded, probably down.
So the "relative Frequency" is the Probability.
This is a bit off-topic, but I was wondering if it is possible to calculate the most probable length of a matchstick. I figured out that the size must be between 2 * sqrt(2) and 2 * sqrt(5), given the frequency table.
I know it is impossible to calculate it for sure, but with the frequency table and some statistics I think it is possible to give a better estimation of the length than I did.
That sounds like a good one,I'm off now for the weekend-railtrip.
So I'm having something to think about.
More to come....
Ok if you want to figure out the probable length, round off the relative frequencies to
#lines__prob.
__0_____0
__1_____1/12
__2_____1/3
__3_____1/2
__4_____1/12
This will make it simpler. The results were close to this anyway.
In a grid there are horizontal and vertical lines. When I use the original results, I get a value of 2.625. Should it be multiplied by 2, sqrt(2), 2 * sqrt(2) or ???
2.625 is smaller than 2 * sqrt(2), the minimum length.
What are you calculating?
I think you have to do it in two steps.
First you need to calculate the probabilities for the match crosses X-Lines. (for all possible X) and that for all possible length of a match.
Now do for each length:
Plot the possibilities for each X ,that way you get a curve (in German called "Normalverteilung") .
You now have several of those curves
In the second step plot the observed frequencies/possibilities in the same way.
Now find that calculated curve that matches the observed one the best and you have your best guess for the length of the match!
At least that'S what I figured during the trainride;-)
I figured some curves representing the probabilities for different length of a match stick (in steps of .1 cm)
See image, the thick red line is the sample (which was much to small). It seems that the green line matches best (4.2 cm).