So on the left over here, I have the data set that we're interested in a forecast of GDP growth in America based on economist. So we're first asked to finding the minimum value in this series. And I went ahead and reordered these. This Siri's just so it's easier for me to visualize and see what exactly is going on with this data, because I reordered it. I was able to find the minimum value really easily.
The minimum value would be the first, uh, value here. So 0.4. Okay, So at 0.4 and it was really easy to see the maximum value again because I already reordered this data and I have the value of 3.5 as my max over here, so Oh, that doesn't look good. My max is three point five. That doesn't look great either, but we'll continue.
So, my mean is going to be the sum of all my observations over the number of my observations. So if you count out all of these, all the number of observations you're going to get that your end is equal to 30 okay? And then you're going to get that the sum of all observations. This is a fancy way of writing. The sum is equal to ah, 69. So you're mean is going to be the result of 69 over 30 which is approximately equal to 2.3.
So you're mean is about 2.3 now for your median? Ah, you're just basic. Or I would just start crossing from the top or bottom. Or what you can do is, uh, find the the exact value in which the median lies. So you can take because the medium is the 50th percentile. You can take 50 over 100 which is 1000.5, take 50 over 100 and then multiply it by the end, which we figured out was 30 and that is equal to 15.
So because that is an even number we're going to or an integer we're going to take the value in between 15 and 16 or the values of 15 and 16 and take the average of them. So here is the value of index. At 15 the value index that 16 is 2.5, both of them are 2.5. So we're going to take the average of the 22.5 plus 2.5 divided by two is equal to 2.5. So we get that our median is 2.5.
Okay, Now our mode, we're basically going to scan through our data set and figure out which data point which individual point occurs most frequently. Okay? And we find that the the the value with the most that is most frequent is 2.7, So I remote is 2.7. Okay? Now, to find out my first and third corps tiles, I'm basically going to do the same thing I did for the median. OK, I will take 25 divided by 100 which I know is 1000.25 and multiply by my end, which is 30 which is equal to 70.5 7.5. Sorry, not 70.57 point five.
Okay. And that means I'm going to take the value at the eighth index and the seventh index and average them. Okay, so 12345123456 seven. Okay, so seven is 1.9 and eight is, too. So I'm going to take the average between 1.9 and two and divide by two, which yields 1.95 Okay, all right.
And now we're going to do the same thing for the 75th percentile or ah, the third quarter mile. Okay, take the ah percentile in decimal form. Multiply it by my end, which is 30 which yields 22.5. Okay, and this appears should not be an equal sign. That should be an arrow.
Um, because those two aren't equally each other. So I'm going to find the 22 23rd indices and average them. Okay, so I'm going to count 1231234 all the way down until I get until I get to 2.8 and 2.8 and the average of 2.8 and 2.8 is 2.8. So I get that. My 75th quartile is 2.8.
Now. This question about whether the economists are optimistic or pessimistic about economic outlook depends on how you view optimism and pessimism. But because all of these data points are positive, that means that there's economists forecast a growth in GDP, which is a good thing. So I would say that there is a positive outlook provided by the economists. Thanks for watching.