00:01
Hey there, welcome to numerade.
00:03
We are asked to approximate the mean and standard deviation here of this following frequency distribution, looking at the high temperature values for a summer month in a city.
00:17
So we're going to treat this data as the population.
00:20
So let's start with our mean.
00:24
What we know is that our mean equals the population mean, which is mu, which equals the sum of our frequency.
00:32
Times x divided by our sample size in which we're given a large sample size here of around 2 ,754.
00:46
Therefore, we're going to get a mean here of around 80 .3.
00:55
All right.
00:57
Now for our standard deviation in which we're going to denote this as sigma.
01:03
So therefore, sigma equals the square root of.
01:06
So the sum of square, so x minus the mean of 80 times their frequency, divided by our sample, or sorry, our population size, 2 ,754.
01:29
Therefore, we're going to punch this into our calculator, giving us a standard deviation here of exactly 9 .0.
01:40
All right? awesome.
01:44
So that would be our mean and standard deviation and so we would have to confirm if this will be bell -shaped but we would need to know our frequency histogram so therefore we would need to see if it's bell -shaped like so okay so remember next time to attach your frequency distribution but what we can work on now is basically part c so based on empirical rule 95 % of days in a month will be between what two times so this will correspond, 95 % will correspond into two standard deviations within the mean.
02:27
So two standard deviations within the mean...