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## High school statistics

# Techniques for generating a simple random sample

AP.STATS:

DAT‑2 (EU)

, DAT‑2.C (LO)

, DAT‑2.C.1 (EK)

, DAT‑2.C.2 (EK)

CCSS.Math: Techniques for generating a simple random sample.

## Want to join the conversation?

- How does one ensure that the random digit table (the list of numbers) is actually random? Isn't using a random digit table almost the same as me writing out "random" numbers because to begin with, that list of numbers was created by me anyways?(10 votes)
- There isn't really a way of knowing if a random digit table is actually random. But if you were to write out a list of random numbers, you could get rid of the "randomness" of the numbers accidentally if you put any thought into the numbers. Or your subconscious might have a method to picking your "random numbers" that you do not know about. So using a random digit table is better since it does not have any apparent bias or method as to how those numbers were chosen.(9 votes)

- At3:41Sal talks about using a random digit table. In his example, he took two consecutive digits and then moved to the next two consecutive digits to get 59, 83, 35, 59, 37, .... Would it have been legitimate to have just moved one digit at a time rather than two to get 59, 98, 83, 35, 59, 93, 37, ...?(6 votes)
- I had the same in mind. The answer is: You have to assign each of your cases a random number to pick that has the same number of digits than your largest case.

Let's say we have 1, 2, 3 .. 25 cases,

then we assign the following random numbers: 01, 02, 03, .. 24, 25.(5 votes)

- At3:32, How is choosing people with numbers assigned from 01 to 80 random? The person which is assigned the number 80 will have the least chance of being chosen because there are so many other 70's, 60's.... Shouldn't a random sample have everything in it equally likely?(2 votes)
- it is equal because the person who is number 76 has the same amount of chance as being chosen with a person who has number 80. They are just numerical place holders to facilitate the generating process.(7 votes)

- What are the methods of obtaining random samples(4 votes)
- will I use this in the real world?(3 votes)
- Could you generate a random digit table by putting the digits 0-9 on a slip of paper, putting those slips in a tumbler, blindly drawing a digit, writing its value on the table, and then immediately placing the digit back in the tumbler before spinning and drawing again?

What are some other examples of how these tables are created?(3 votes)- Yes, this is a possible way to make a random digit table, as long as the slips are replaced. Another example would be to use a calculator function or computer program to generate the random numbers for you. A final example would be rolling a 10 sided die.(0 votes)

- At4:09if you go with the randomly generated list of numbers, do you get a truly random sample if the randomly generated list of numbers has repeated digits.

Eg. if instead of starting with 5983... the number starts with 5959.. Does this lead to any bias in the sample.(2 votes)- Human generated "random numbers" will avoid duplicates, however a true random set of numbers does not take into consideration what any of the numbers before it were it is completely random so a chart could start with repeated numbers and not be biased.(1 vote)

- Are there any other techniques for this simple random sample.(2 votes)
- I want to point out that using a computer to get a bunch of "random" numbers is not good if it really matters that everything actually truly is random because computers cannot
**actually**generate a list of*completely*random numbers.(1 vote) - How does one ensure that the random digit table (the list of numbers) is actually random? Isn't using a random digit table almost the same as me writing out "random" numbers because to begin with, that list of numbers was created by me anyways?(1 vote)

## Video transcript

- [Teacher] Let's say that your school has a population of 80 students in it. Maybe it's not your whole school. Maybe it's just your grade. So there's 80 students in your population and you wanna get an estimate
of the average height in your population and
you think it's too hard for you to go and measure
the height of all 80 students so you decide to find a simple or take a simple random sample. You think it's reasonable
for you to measure the heights of 30 of these students and so what you wanna
do is randomly sample 30 of the 80 students and
take their average height and say, well, that's probably
a pretty good estimate for the population parameter for the average height
of the entire population. So once you decide to do this, you say, well, how do I
select those 30 students and how do I select it so that I feel good that it is actually random? And there's several ways
that you could approach this. One way to do it is associate every person in your school with a piece of paper
and put 'em all in a bowl and then pick 'em out so let's do that. So let's say this is alphabetically the first person in the school. They're on a slip of paper then the next slip of
paper gets the next person and you're gonna go all the way down so you're gonna have 80 pieces of paper. They all should be the same size and then you throw them all, you throw them all into
a bowl of some kind and this seems like a
very basic way of doing it but it's actually a pretty effective way of getting a simple, of getting a simple random sample. So I'll try to draw a little, I don't know, that looks like
a fish bowl or something. Alright, so that's our bowl. And so all the pieces of paper go in there and then you put a blindfold on someone and they can't feel what names are there and so they should pick out the first 30 without replacing them because you obviously
don't wanna pick the same, you don't wanna pick
out the same name twice. And those 30 names that you pick, that would be your simple random sample and then you could measure their heights to estimate the average
height for the population. This would be a completely
legitimate way of doing it. Other ways that you could do it, if you have a computer or a calculator, you could use a random number generator and the random functions on
computer programming languages on your calculator, they
tend to be something, someplace you'll see
something like a math.rand Rand's short for random. You might see something like random. You might see, you might see something like random without anything passed into it. It might give you a number
between zero and one or zero and 100 and you
have to be very careful on how you use this to
make sure that you have an even chance of picking certain numbers but what you would do in this situation if you had access to some
random number generator and it could even pick out a random number between one and 80 including one and 80 is you would maybe line up all the students' names alphabetically and so the first student alphabetically assigned the number 01 and you could just say one if you're using a random number generator but I'll use two digits for it just because it'll be
useful and consistent and in a little bit, we'll
use another technique where it's gonna be nice to be consistent with our number of digits. And so the next one, 02 and you go all the way to 79 and all the way to 80 and then you use your
random number generator to keep generating numbers from one to 80 and as long as you don't get repeats, you pick the first 30 to be
your actual random sample. Another related technique which is a little bit more old school but is definitely the way that
it has been done in the past and even done now sometimes is to use a random digit table. You still start with
these number associations with each student in the class and then you use a randomly
generated list of numbers and so let's say that's our randomly generated list of numbers and it keeps going well beyond this and you start at the beginning and you say, okay, we're
interested in getting, we're interested in getting
30 two digit numbers from one to 80 including one and 80. So one technique that you could use is you start right at the
beginning and you could say, alright, this is a randomly
generated list of numbers. So the first number here is 59. Is 59 between one and 80? Sure is, as long as we, if this was a 01, that would have worked. If this was an 80, that would have worked. If this was a 00, it wouldn't have worked. If this was an 81, it
wouldn't have worked. This would be our, this right over here, that would be our first name that we, you could imagine the same as picking that first name out of the hat, whoever's associated with number 59. Now, you would move on. You get the next two digits. The next two digits are 83. They don't follow into
our range from one to 80 so we're not going to use it then you would look at
the next two digits. So we get a five and a nine. Well, that fits in our range
but we already picked 59. We already picked person 59 so we're not gonna pick 59
again so we keep moving on then we get a 37. Well, that's in our range,
we haven't picked that yet. We do that then we get a 00. Once again, not in our range. I think you see where this is going. 91. Not in our range. 23. It's in our range and
we haven't picked it yet so we're gonna pick the 23. I think you see where this is going. We're gonna keep going down this list in the way that I've just
described until we get, until we get 30 of these. We've just gotten three. We just have to keep on going and this isn't an exhaustive list of all of the different ways
that you can get random numbers but it starts to give you some
techniques in your toolkit and you might say, oh, well,
why don't I just randomly come up with some numbers in my head? And I would really suggest
that you don't do that because humans are famously
bad at being truly random and you might wanna do something like even use something that you
think is a random process but you realize later
that it wasn't as random as you thought. So once again, multiple techniques but these are some of the
I would say best practices for actually generating
a simple random sample.