00:01
For this problem, we are told that the following data, which have copied into a more convenient table form, represents the high temperature distribution for a summer month in a city for some of the last 130 years.
00:12
We are to treat the data as a population.
00:15
And for the only question that was included here, we are asked to approximate the mean in standard deviation for temperature.
00:21
So the way that we want to go about doing this is by beginning, or we'd start off by effectively translating our table.
00:30
Here to a form where first of all we'll have essentially we'll be translating this to a probability distribution where we have x and p of x where i'll be making the necessary changes momentarily but the first thing that we want to do is convert all of our days counts into relative proportions so i'm just going to copy down the data into my software here and then we want to divide the those values by the sum of those values.
01:05
This is, as i said, we're just basically figuring out what is the total number, and then we're taking each one of the day counts and dividing that by the total to get a relative frequency.
01:19
And just to make this a little bit easier to deal with, i'll round everything to three decimal places.
01:24
So we have p of x is 0 .009, 0 .085, 0 .5.
01:33
0 .43, 0 .03, 0 .073, and 0 .003.
01:43
And our x, for each one of these categories, would be the midpoint of the bin, so to speak.
01:49
So we'd have 55, 65, 75, 75, 85, 85, and 105.
01:58
So, now that we have our frequency distribution, what we can do is find that the mean value would be equal to the sum of each possible x value times the probability or the relative frequency of that x value...