WEBVTT Kind: captions; language: en-us NOTE Treffsikkerhet: 85% (H?Y) 00:00:00.000 --> 00:00:07.000 In this video I want to give some clarifications about how to think about the median or indeed any 00:00:07.000 --> 00:00:08.900 other quantile. NOTE Treffsikkerhet: 80% (H?Y) 00:00:09.500 --> 00:00:19.400 Here you can see several data sets, small data sets, all of which have a median equal to 3. On the 00:00:19.400 --> 00:00:27.400 left hand side there are data sets with an odd number of data points. So they all have a middle 00:00:27.400 --> 00:00:34.700 point, which therefore is the median. And on the right hand side. There are data sets with an even 00:00:34.700 --> 00:00:39.150 number of data points, so they don't have a middle point. NOTE Treffsikkerhet: 83% (H?Y) 00:00:39.150 --> 00:00:48.599 And to determine the median if the two points aren't equal, then we have to calculate their average. 00:00:48.599 --> 00:00:56.000 So you can pause this video and check these datasets until you are convinced that they all have a 00:00:56.000 --> 00:01:04.000 median of 3, and then the question is what is a general statement we can make that is true about 00:01:04.000 --> 00:01:09.199 the median and it's true in each one of these data sets. NOTE Treffsikkerhet: 91% (H?Y) 00:01:09.199 --> 00:01:19.000 If you think about it, you will see that the statement you can make about the median is that at 00:01:19.000 --> 00:01:29.200 least half of the data are less than or equal to 3, that is the median, and at the same time at least 00:01:29.200 --> 00:01:39.600 half of the data are greater than or equal to 3. So you need to have at least an equal. NOTE Treffsikkerhet: 91% (H?Y) 00:01:39.600 --> 00:01:48.100 Because we don't know how many data points are actually equal to the mean in a given case or indeed 00:01:48.100 --> 00:01:51.800 if any data points are exactly equal to the mean. NOTE Treffsikkerhet: 91% (H?Y) 00:01:51.800 --> 00:01:59.900 Instead of these two sentences, we could use the equivalent set below that no more than half of the 00:01:59.900 --> 00:02:06.199 data are greater than 3. And no more than half of the data are less than 3. NOTE Treffsikkerhet: 90% (H?Y) 00:02:06.199 --> 00:02:13.200 In fact, these four statements are all necessarily true for any data set that has a median of 00:02:13.200 --> 00:02:14.300 three. NOTE Treffsikkerhet: 85% (H?Y) 00:02:14.300 --> 00:02:23.600 And more generally for any value of median X. If the median is X then it must be true that at least 00:02:23.600 --> 00:02:31.700 50% of the data are less than or equal to X and at least 50 % of the data are greater than or 00:02:31.700 --> 00:02:33.800 equal to X. NOTE Treffsikkerhet: 81% (H?Y) 00:02:34.400 --> 00:02:41.500 As well as no more than 50% of the data are greater than x and no more than 50% 00:02:41.500 --> 00:02:48.600 of the data are less than x. So these are the general statements that amounts to the definition of 00:02:48.600 --> 00:02:49.950 the medium. NOTE Treffsikkerhet: 91% (H?Y) 00:02:49.950 --> 00:02:56.400 This isn't limited to the median. It can be used for any other quantile. So for example, for the 00:02:56.400 --> 00:03:06.300 first quartile. If the first quartile equals X then we can say that at least 25% of the data are 00:03:06.300 --> 00:03:15.100 less than or equal to X and at least 75% of the data are greater than or equal to X. NOTE Treffsikkerhet: 75% (MEDIUM) 00:03:15.700 --> 00:03:24.600 Alternatively. No more than 75% of the data are greater than x and no more than 25% of the data 00:03:24.600 --> 00:03:26.900 are less than x. NOTE Treffsikkerhet: 91% (H?Y) 00:03:27.700 --> 00:03:35.700 And you can use these statements for any other quantile by substituting 25 and 75 with the quantile 00:03:35.700 --> 00:03:37.700 of your liking.