00:01
Okay, so we've got a question about two sensors measuring the water levels in a river.
00:10
And we've got two different sets of data.
00:12
We've got sensor a and sense b.
00:13
So it says to compute the sample mean, median mode and midrange.
00:17
Now, i'll quickly explain what all of those are and how you calculate them, but then i'll just give you the answer rather than explicitly writing everything out because it will take forever.
00:26
But hopefully this will give you everything you need.
00:29
So the sample mean to find the mean, you just add up on, so it's the sum of all the data points divided by how many there are.
00:43
So here there are 10 measurements for each sensor.
00:51
There's over 10 different days.
00:53
We've taken a measurement on each day.
00:55
And so you add all the numbers and divide by 10.
00:58
The median is the middle value when it's all in order of ordered data.
01:09
So you line them up from smallest to biggest and you select the middle one.
01:13
If there's an even number, then you go halfway between the two middle values.
01:19
The mode is just the most common one, the one that appears most often in the set.
01:28
The mid range is given by the smallest, it's the midway point between the smallest and largest values.
01:41
So the smallest plus the largest divided by two.
01:44
We're also asked for the standard deviation and variance.
01:47
So the variance is, it's a measure of the spread of the data.
01:52
And it's the sum over each of the data points, which i call xi, the difference between that and the number.
01:59
Mean of the data, which we said up here, squared, and then divided by the sample size minus 1, and the standard deviation is just the square root of the variance.
02:14
So that's what all the things are, and then i'll now just list what they are for all of these things.
02:19
So for sensor a, the mean is given by 5 .74.
02:27
The median is 5 .55...