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Problem 42 Hard Difficulty

The size of the home ranges (in square kilometers) of several pandas were surveyed over a year’s time, with the following results.
a. Sketch a histogram and frequency polygon for the data.
b. Find the mean for the data.

Answer

a. Draw 7 adjacent rectangles, each having width of 0.4 (the width of each range), and as height, the corresponding frequency. Label each with the label from the table.
b. 1.0875 $\mathrm{km}^{2}$

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Video Transcript

this question gives you a table that shows the area of the home ranges for several pandas, its frequency table. And it wants us first to create a hist a gram. So we know that our bins here are of length 0.4. And what I'm gonna do is I'm gonna start by drawing some axes, and, uh, the way I want to draw the bins is to be left endpoint inclusive and write a in point exclusive. So if I have 0.1 to 0.6, the bar here is going to include 0.1 all the way up to 0.5 and not Sarah 0.6, which is what we want. So I do like that and we'll go through this whole thing. So are left endpoints as we go along. 0.10 point six, 1.1, 1.6, 2.1, 2.6 3.1 All the way up to our last endpoint is Super Five soldiers, right? 3.6. Here we will have that, um and then I'll scale my y axis to be go up by threes like this so that this will be as well but high. This would be 12. So let's go ahead and draw this out on our first Been. The 0.1 is there from five. There are 11. So I will bring this bar up to 11 in our next been there are 12. So go there. This is not gonna be perfect. It's hand drawn, but you get the idea. Then we have seven in 1.1 to 1.5 six and 1.622 points. Zero to in 2.1 to 2.5. So right about there and then the next ones, we have one and one. The question also wants you to draw a frequency. Probably gonna remember. We do that by connecting them mid points of every, uh, bar to the mid points of the bars. That would be next to it on the ground, the X axis. So I go ahead and do that. Get something that looks a little bit like this again. It's not gonna be perfect, Especially since I'm drawing it on a computer. But it would look something like that, and that's gonna be your frequency polygon. Next. It wants us to find the mean We know. We estimate means from frequency tables using the formula. Uh, X bar equals the sum of the value times the frequency over the sum of all the frequencies. Now, the value here were given ranges, but the value here that we're gonna use is the midpoint of each range. Um, the midpoint of the trains are syrah 0.3, 0.8, 1.31 point 82.32 point eight and 3.3. And again we have the frequencies 11 12 76 to 1 and one. And now I'm going to add a call in to this table X times f. And I'm gonna just multiply these two columns together. So we'll get 3.39 point 69.1, 10.84 point six and then 2.8 and 3.3. Now all that's left to do is some up the F column in the X column and the XF column. When we add all the frequencies together we get 40. I make sense where you have 40 data points and then we add on the X efs. Together we get 43.5. So explore is gonna be 43.5. She's 43.5, divided by 40 which we find is 1.87 five. And remember, art, uh, units are in square kilometers, so are averages 1.75 square kilometers that your final answer