00:01
Okay, so in this question, we know that the total number of observations is going to be 114.
00:07
So we can say this, 7 plus whatever f1 is, plus 17, plus f2, plus 32, plus 6, and then plus 10 is equal to 114.
00:49
So let's add all this up.
00:50
7 plus 17 plus 32 plus 6 plus 10 is 72.
01:00
And we know total it's going to add up to 114.
01:02
So if i subtract that 72 from the 114, then i know that f1 plus f2, whatever those are, we don't know like how it's distributed, but whatever we get when we add those together must be equal to 42.
01:18
Okay, so now we're going to use this formula because we're given like the mode, but we're not told the mean.
01:34
So most of the questions usually give you the mean, but this time we're just given the mode.
01:39
So we have to use this formula here.
01:40
And let me just tell you what everything stands for.
01:42
So z is going to be the actual mode.
01:45
So we'll just replace that.
01:48
And our mode is 85 .7.
01:53
So we can say 85 .7 equals.
02:01
And then we have l and l is representing the lower limit of the of the model class so that's wherever the mode is following or sorry coming from so because we're looking at 85 .7 we're looking at this class here so the lower limit is 85 plus then we have f0 f1 and f2 so since this is our like mode class this is gonna be our f1 the one before it is f0 and the one after it is f2 and um we're just giving the frequencies so f1 the frequency is 32 minus f0 we don't know what that is but that's like our f2 in the problem not to be confused with the f2 i'm using in the formula over two times f1 is 32 minus f0 again which is f2 in the original problem unrelated to the f2 in this formula here this f2 means 6 so we have then minus 6 and then last is time c which is the size of the class interval so 10 because each of these is 10 wide okay so this actually makes it pretty simple because we're going to be able to solve for f2 straight from here it's just going to require some computations.
03:55
So let's start with two times 32 and we'll subtract the six also.
04:00
So i'm working on this denominator.
04:01
So i have 32 minus f2 over 58 minus f2 times 10.
04:24
And then they have 85 plus that.
04:29
And that's equal to 85 .7.
04:37
I'm going to distribute now the 10.
04:41
So i have 85 .7.
04:42
Actually, you know what? let's just subtract this 85 over.
04:46
So i'm going to have 0 .7 equals.
04:51
And now i'm going to multiply out the 10.
04:53
So 320 minus 10 times f2 over 580 minus 10 f2.
05:21
Then we're going to take this whole entire denominator here, multiply it to the other side.
05:29
So we have 580...