Relative frequency is probability

 Thirteen students tossed a coin ten times and counted the number of heads obtained.


The results were recorded on the whiteboard. Note that the mode is "five heads" and not one or zero in the second column: those are frequencies. The most frequent result was five heads.


The above spreadsheet is the same data as on the whiteboard. The relative frequencies are the probabilities.

Expand the sample size to 1000 students tossing a coin ten times and here is one of the relative frequency results obtained. 

Expand the sample size again, to infinity and beyond, and one will eventually arrive at the mathematically predicted outcome for ten tosses of a coin. 0.25 or 25% of the tosses will be five heads. 21% will be either four or six heads. Zero, one, nine, and ten heads are very rare. This distinction between what is randomly expected to occur (three, four, five, six, and seven heads account of 89% of the expected results) and what is rarely expected to occur will underpin work on whether a sample is expected to be drawn from a population or not. 

For now, the relative frequency (which is the frequency divided by the sample size) is the probability of an outcome or result in statistics. 

104 cars of 250 cars passing the college were Toyotas. 104 ÷ 250 = 0.416 thus there is an estimated 41.6% probability any given car that passes the college will be a Toyota. This also likely implies that around 40% of the cars on Pohnpei are Toyotas. Relative frequency is probability. 


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