Learn AISL 4.1.1 Discrete v continuous data in this free IB Mathematics Applications & Interpretation (AI) video lesson for SL 4.11—Expected, observed, hypotheses, chi squared, gof, t-test.
Learn AISL 4.1.1 Discrete v continuous data in this free IB Mathematics Applications & Interpretation (AI) video lesson for SL 4.11—Expected, observed, hypotheses, chi squared, gof, t-test.
The video explains the difference between discrete and continuous data. Discrete data can only take certain values, such as the number of students in a class or shoe sizes, while continuous data can take any value, like height or time.
Key examples include:
Understanding these distinctions is crucial as they will frequently appear throughout statistics topics.
00:00Hi everybody. So in this
00:02lesson we're going to look
00:03at the difference between discrete
00:05and continuous data. Now I've
00:07two kind of loose definitions
00:08here. Discrete data can only
00:11take certain values and continuous
00:13can take any value. Now
00:16I find the best way
00:17to kind of explain the
00:18difference between the two is
00:19to get a lot of
00:20examples and then decide which
00:23one is or into which
00:26category it goes. Discrete or
00:28and then kind of discuss
00:29them a little bit. So
00:30what I'm going to do
00:31is I'm going to move
00:32them into the correct category.
00:34I suggest you have a
00:35guess. Well, see if you
00:38know the answer, but even
00:39if you don't know the
00:40answer, have a guess. Choose
00:41one for each of these
00:44before I do it. So
00:45the number of students in
00:46a class does it go
00:47into discrete or continuous? Well,
00:50it goes into discrete because
00:52you can only have a
00:56certain
00:56number of students in a
00:57class, it's either going to
00:58be 10 or 11 or
01:0012 or 13 or 25
01:01or 26 or whatever, you
01:02can't have 22 .345682 students.
01:07Are you can't even have
01:09five and a half students
01:10or 10 and a half
01:11students or whatever? So it
01:13has to, it is discrete,
01:14it is not continuous. Shoe
01:16size, shoe size is also
01:20discrete. Now a common misconception
01:22is that
01:24Screete is like whole numbers
01:26or integers. And it's like
01:28shoe size would be, let's
01:30say six or seven or
01:32eight or nine. But it
01:34doesn't have to be integers.
01:36For example, you could have
01:37shoe size of 6 .5,
01:407, 7 .5, 8, 8
01:44.5. Now even though I
01:45have 0 .5, it's still
01:48discrete because it's jumping. It
01:50goes from 6 .5 to
01:517.
01:52seven to seven or five.
01:53You kind of six point
01:54five, two, three, four, two,
01:57eight, nine, seven, whatever. Okay,
02:00so just, just be clear.
02:02It's not, discrete does not
02:04mean a whole number. It
02:05just means certain values. Okay,
02:08now here I have to
02:08liberty put in one that's
02:11similar to shoe size or
02:13shoe sizes to screat, foot
02:14length is continuous, because you're
02:18the length of your foot
02:20Yes, it can, it can
02:22be anything. It can take
02:23any value. Your foot doesn't,
02:27it's not like it's 20
02:30centimeters and then the next
02:31day, it's 21 centimeters or
02:34even the next second, then
02:35it goes to 22 centimeters.
02:37Your foot doesn't grow like
02:38that. It grows continuously. Height
02:42is similar. You don't just,
02:44you don't just suddenly get
02:46a foot taller or even
02:47a centimeter taller.
02:48or even a millimeter taller
02:52or even the smallest length
02:53you can think of, it
02:55happens continuously. Now I actually,
02:59I like to say that,
03:01let's think of height, let's
03:03say six foot. I like
03:05to sometimes ask the question,
03:06how many people in the
03:08world are six foot tall
03:11exactly? And the answer is
03:13zero. Nobody, there is nobody
03:16in the
03:16world that is exactly six
03:18foot tall. It's it's mathematically
03:22correct to say it it
03:24it is zero people because
03:26you're either going to be
03:27a tiny tiny little bit
03:28more than six or a
03:30tiny tiny little bit less
03:31than six. Now if I
03:32said how many people are
03:34between let's say between between
03:40five point nine nine nine
03:43nine feet
03:44and 6 .0001 feet then
03:51yeah there could be many
03:54people between this and this
03:58in terms of height but
03:59there's zero people that are
04:01exactly six foot and that's
04:02quite important. Okay time to
04:05get to school how long
04:06does it take you to
04:06get to school? That's continuous
04:09because time is continuing
04:12It's not, now if it
04:14said time rounded to the
04:17nearest minutes, then yeah, that's
04:19discrete because it's either five
04:20minutes or six minutes or
04:2110 minutes or 20 minutes
04:22or 21 minutes. But if
04:23it's just time, there's always
04:26that little difference. It's never
04:28exactly 10 minutes. It's like
04:3010 point something. Olympic 100
04:34meter final times now, I've,
04:37I'm deliberately putting in one
04:38set of slightly tricky.
04:40This is discrete and the
04:42reason is because if you
04:45watch the Olympics they measure
04:46them to the nearest hundredth
04:48of a second. So the
04:50world record is like from
04:51Usain Bolt 9 .5, I'm
04:57struggling with this. See there
04:59are 5, 8 or 5,
04:599. I'm going to go
05:00with 5, 8. Hope I'm
05:02correct there. So the 100
05:04meter final times it's measured
05:07to the nearest hundredth of
05:08a second.
05:08second. You saying both did
05:10not run it in exactly
05:119 .58 seconds? It was
05:14rounded to the nearest hundredth
05:15of a second. And sometimes
05:16you'll see two people finish
05:18with the exact same time.
05:20And that's when you get
05:22what they call a photo
05:23finish. And they actually need
05:24to look at the photo
05:26to see who actually crossed
05:27the line first. Okay, coffee
05:32temperature. Well, if you've seen
05:36my lesson,
05:36on exponential functions, you'll see
05:39that, well, maybe that doesn't
05:41mention continuous, but the temperature
05:43is continuous, because it continuously
05:46drops, it gets cooler and
05:47cooler and cooler. It doesn't
05:48suddenly go from 80 degrees
05:52to 70 degrees, or even
05:54from 80 to 79, it
05:56just slowly continuously gets cooler.
05:59Age in years, it's discrete,
06:02because you do jump, you
06:04jump from
06:0416 to 17 and then
06:09from 17 to 18 that's
06:11in years. Time you've been
06:13alive, that's continuous. Number of
06:16goals scored, that's discrete. You
06:19either scored five goals or
06:21six goals or seven goals,
06:22you didn't score five point
06:23two goals or anything like
06:24that. And the mass of
06:26apples in a shop, well
06:28mass is, mass is continuous.
06:33Because again, it doesn't jump.
06:38It's not like one apple
06:40is 60 grams and then
06:45another apple is 62 grams.
06:49Now if the shot might
06:50weigh it to the nearest
06:51gram, but really the mass
06:54of the apple is continuous
06:56and you could have an
06:57apple that weighs 6 .1234,
07:0056.
07:01for eight, nine, ten grams,
07:02whatever. Okay, that's discrete, be
07:07continuous. Hopefully it's clear. Yes,
07:11it's very important. And it
07:15will be coming up in
07:17all along the statistics topic.
07:21You will see discrete continuous
07:22data. So make sure you
07:23understand what the difference is.