WEBVTT 00:00.750 --> 00:03.800 Hello and welcome back to our costs about summary statistics. 00:03.800 --> 00:06.060 So why are some of these statistics useful. 00:06.090 --> 00:13.170 Um yeah let's assume you have an array with 1000 or 10000 elements and you want to summarize these elements 00:13.200 --> 00:15.080 in one or two numbers. 00:15.230 --> 00:21.790 And for this task an umpire provides us with many options how to summarize in large numerical arrays. 00:21.840 --> 00:24.950 So first of all that's the important umpire. 00:24.990 --> 00:32.770 Then we create uh eleven random integers in the range one to one hundred and assign the variable A. 00:34.080 --> 00:43.560 Then we start a net we can see so now we have uh the lowest numbers eighteen forty eight and the highest 00:43.570 --> 00:45.230 integers ninety nine. 00:45.510 --> 00:48.480 And then we can calculate the maximum of our array. 00:48.510 --> 00:54.560 So the highest element with the method top Max it's ninety nine here. 00:55.650 --> 01:00.180 And we can also do this trap here by applying the function and picked up Max. 01:00.180 --> 01:03.650 So this gives us uh the same result. 01:04.020 --> 01:06.230 And earlier we learned about the function Max. 01:06.240 --> 01:08.400 So we can also apply the function Max. 01:09.600 --> 01:10.770 So we can see them. 01:10.840 --> 01:16.710 Yeah actually three alternatives to calculate the maximum and also with the minimum they are the same 01:16.710 --> 01:17.720 three alternatives. 01:17.750 --> 01:17.970 Um. 01:18.020 --> 01:20.540 And I only show here the number pi method. 01:20.590 --> 01:31.170 Duckman so I would expect 18 and we can also calculate the mean of all elements that end put up mean. 01:32.570 --> 01:39.380 So it's seventy four are we use the method that mean should be the same. 01:39.810 --> 01:42.150 And we can also calculate the median. 01:43.170 --> 01:45.000 So let's run it. 01:45.230 --> 01:45.800 Eighty four. 01:45.810 --> 01:50.970 So what is uh the median so the median gets less. 01:51.020 --> 01:57.620 Actually the point where 50 percent of all other points are lower than and 50 percent of all elements 01:57.620 --> 01:58.910 are higher than the median. 01:58.910 --> 02:04.200 So we have eleven elements the median is the sixth element. 02:04.200 --> 02:09.060 So we have five elements which are lower than the median and five elements which are higher than the 02:09.060 --> 02:09.870 median. 02:09.870 --> 02:12.020 So this is a very simple words. 02:12.030 --> 02:20.050 And in the simple example here the median and we can also calculate the standard deviation of our lower 02:20.070 --> 02:21.430 elements. 02:21.540 --> 02:22.980 So it gives us 24. 02:23.790 --> 02:28.420 So the standard deviation is a measure of the liability of our elements. 02:28.920 --> 02:35.510 So if all elements would be let's say 50 our standard deviation would be zero. 02:35.520 --> 02:40.470 If the variability is quite high so then also the standard deviation is high but I don't want to go 02:40.470 --> 02:46.270 into statistical details here and our variance is also a measure of the reliability. 02:46.320 --> 02:50.360 And actually standard deviation is the square root of variance. 02:50.370 --> 02:53.260 But this is not a cross about statistics actually. 02:53.370 --> 02:56.910 And we can also calculate the person tile off our array. 02:56.920 --> 03:01.540 So let's say the here the function and p dot percentile. 03:01.650 --> 03:09.780 We have our array and then we say we want to determine our 10th percentile and it's forty eight. 03:09.780 --> 03:10.420 So what. 03:10.440 --> 03:12.120 What does it mean exactly. 03:12.120 --> 03:19.350 So the 10th percentile means that this is the point actually where 10 percent of all the other elements 03:19.350 --> 03:22.350 are lower than this point and 90 percent are higher. 03:22.350 --> 03:26.660 So you can see here we have the 10th percentile forty eight. 03:26.730 --> 03:31.110 And while that one element is lower and the other nine elements are higher. 03:31.170 --> 03:32.780 So this is an easy words. 03:32.790 --> 03:44.060 And the person type and also we can calculate the 19th percentile so it's 98 and you can see here 90 03:44.070 --> 03:47.150 percent of our elements are lower than the 19th percentile. 03:47.160 --> 03:54.210 So we have four main elements and only 10 percent or in this case one element is higher than the 19th 03:54.210 --> 03:58.920 percentile. 03:58.980 --> 04:05.550 All right so let's again create a an array with eleven random integers in the range between 1 and 100 04:05.580 --> 04:11.080 and let's call it a and we create another array with them. 04:11.100 --> 04:15.770 Eleven random integers in the range 1 and 101 but you can see here. 04:15.840 --> 04:22.080 So we have a different random seed and I would expect now that we get different random numbers here 04:22.080 --> 04:26.380 for our array B there can see here. 04:26.400 --> 04:28.180 So the arrays are different. 04:28.320 --> 04:33.810 Now we can calculate the covariance of A and B with the function and p dot Cove 04:37.470 --> 04:42.880 and the covariance is actually measure how to erase the two sequences of numbers that move together 04:43.360 --> 04:45.010 so he it gives us a matrix. 04:45.040 --> 04:51.450 Um the first element is actually the parents of element on Empire A. 04:52.330 --> 04:56.600 Then here we have the variance of our array B. 04:56.650 --> 04:58.170 And here we have two times them. 04:58.180 --> 05:00.770 The covariance of A and B. 05:00.910 --> 05:08.110 So as you can see here is the minus sign both sequences should be kind of negatively correlated and 05:08.350 --> 05:16.420 we can better see this then by calculating the correlation coefficient by using the function N.P. dot 05:16.420 --> 05:20.130 Car Co F so also here we get here. 05:20.140 --> 05:24.870 This is the correlation of array avers itself. 05:24.940 --> 05:25.860 It's 1 now. 05:26.080 --> 05:32.560 So it's no surprise that a is perfectly correlated with a B you get the correlation of our repeats with 05:32.650 --> 05:33.990 itself. 05:34.060 --> 05:35.860 And here we now we have two times. 05:35.950 --> 05:39.350 The correlation of a and b and it's negative. 05:39.370 --> 05:46.330 So whenever a increases B should have a tendency to decrease and the correlation coefficient as they 05:46.330 --> 05:53.650 are between minus 1 and 1 and minus 1 means a perfect negative correlation and one means the perfect 05:53.650 --> 05:58.850 positive correlation and correlation of zero means actually no correlation. 05:58.870 --> 06:05.830 So he can see we have a slight negative correlation between num PIRA a and b and actually because we 06:05.830 --> 06:12.010 created both arrays Yeah independently and randomly we would expect actually to have zero correlation 06:12.010 --> 06:13.230 between those two. 06:13.330 --> 06:19.050 And if you would increase the the amount of elements in each array so let's say instead of having eleven 06:19.110 --> 06:25.700 one thousand elements then I would assume that we get a correlation which is very close to zero. 06:25.720 --> 06:26.920 All right so this is it. 06:26.950 --> 06:29.800 This wasn't a quick overview or a summary statistic. 06:29.810 --> 06:35.590 So there are a lot of options here none pi and in the next session with the US again with the realisation 06:35.620 --> 06:37.450 and regression with an umpire. 06:37.510 --> 06:38.320 See you there.