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# Two-way relative frequency tables

Relative frequencies show how often something happens compared to the total number of times it could happen. In our example, we calculate the relative frequency of accidents for SUVs by dividing the number of SUVs that had accidents by the total number of SUVs. This gives us a percentage or fraction that tells us how common accidents are for that type of vehicle.

## Want to join the conversation?

• what does relative frequency means? •  Relative means in relation to each other. So if I have 1 car crash and three cars that didn't crash, I would have a 1 in 4 chance (1 out of 4 total cars) of crashing and a 3 in 4 chances that I wouldn't crash. Maybe I have 14 crashes out of 100, which if you do the math, simply reduces to mean that 1 out of 7 total vehicles, will, on average, experience some form of an automobile accident (I could have used 25 out of 100 here, or something easier, but I decided to step up the game) . It's comparing the total number of events within a specified column--say only the column on Ford motor vehicles (this is just an example), and comparing the percentages of each event happening. It's just isolating each variable and comparing the part to a whole within the context of one column. Hope that helps.
• At about , I don't understand the whole rounding to the nearest hundredth thing...? And why does he round up to 0.78? I'm so confused! •  I assume you really do not understand rounding? It does not matter if it is to nearest whole number, tenth, hundredth, etc.
The key to rounding as you are learning it in the beginning is to know what place you are rounding to and what the number to the right of that is.
So if it is to the nearest hundredth, underline the number that is two to the right of the decimal. All the numbers to the left of the underlined number stay the same. My underlined number has two choices - either stay the same or move up one. So the one number to the right of our underlined number tells us which one -
If it is less than 5, then we stay the same
If it is 5 or greater, then we move up one.
So with his .776, we underline the second 7 and ask ourselves does it stay a 7 or move to an 8 (since 6 is after this seven, we choose to move up to an 8 and write .78.
The different one is a 9, if we have to round up to a 10, we have to change the number to the left of our number and move it up one.
Hope this helps on rounding
• Why on earth does the quiz question have you fill in all of the relative frequencies when only giving the row and column totals when you never explained how to do it? Thats really really annoying. • I'm having trouble understanding this, any advice? • OK! Great video, I understood nicely. But I have a question that maybe isn't the subject. Any way: I see why he sum 28 + 97 = 125, and then 28/125. Its shows the percentage of the accidents involving SUV's vehicles last year. ok!
But what means 28/97, how can I think about that? does It make any sense ? • i dont understand this at all he only does one subject and he adds it up by downwords but some of the tests its adding it sideways and i always end up not passing and its my last test on it im just confused • The reason we add by column is because we are told to fill in the column relative frequencies.

So, we divide each column by the column total.
For example, the relative frequencies for the SUV column will be:
` 28∕(28 + 97) ≈ 0.22`
` 97∕(28 + 97) ≈ 0.78`
`(28 + 97)∕(28 + 97) = 1.00`

This tells us that 22% of the SUVs in this sample were involved in an accident the past year.
• I assume you really do not understand rounding? It does not matter if it is to nearest whole number, tenth, hundredth, etc.
The key to rounding as you are learning it in the beginning is to know what place you are rounding to and what the number to the right of that is.
So if it is to the nearest hundredth, underline the number that is two to the right of the decimal. All the numbers to the left of the underlined number stay the same. My underlined number has two choices - either stay the same or move up one. So the one number to the right of our underlined number tells us which one -
If it is less than 5, then we stay the same
If it is 5 or greater, then we move up one.
So with his .776, we underline the second 7 and ask ourselves does it stay a 7 or move to an 8 (since 6 is after this seven, we choose to move up to an 8 and write .78.
The different one is a 9, if we have to round up to a 10, we have to change the number to the left of our number and move it up one.
Hope this helps on rounding • I'm so confused... I tried the method on my own problem and I got it incorrect? I followed all the steps and I triple-checked!! Is this just me? :( • In the problems on the real exercises,all the data combined does not equal 1. I'm confused. • Okay so basically, I'm doing the Khan Academy exercises for this and each time I go through it I use this method Sal uses but I seem to only get the 1st and 4th question right. The 2nd and 3rd are always incorrect, am I using the wrong method? Is there a bug in the exercices, please help me out as fast as possible. • I think it has to do with whether they ask for the row relative frequencies, or the column relative frequencies.

For example, let's say we have a table that looks like this:
`75 8`
`84 45`

For the row relative frequencies we divide each data point by the sum of the data in that row:
`75∕(75 + 8) 8∕(75 + 8)`
`84∕(84 + 45) 45∕(84 + 45)`
Rounding to two decimals, we get
`0.90 0.10`
`0.65 0.35`
Notice that each row adds up to 1.00

Similarly, for the column relative frequencies we divide each data point by the sum of the data in that column:
`75∕(75 + 84) 8∕(8 + 45)`
`84∕(75 + 84) 45∕(8 + 45)`
Again rounding to two decimals, we get
`0.47 0.15`
`0.53 0.85`
Now each column adds up to 1.00