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Problem 26 Hard Difficulty

Team batting averages for major league baseball in 2015 are represented below. Find the variance and standard deviation for each league. Compare the results.
$\begin{array}{lcccc}{} & {\mathrm{NL}} & {} & {\mathbf{A} \mathbf{L}} & {} & {} \\ \hline 0.242-0.246 & {3} & {0.244-0.249} & {3} \\ {0.247-0.251} & {6} & {0.250-0.255} & {6} \\ {0.252-0.256} & {1} & {0.256-0.261} & {2} \\ {0.257-0.261} & {11} & {0.262-0.267} & {1} \\ {0.262-0.266} & {11} & {0.268-0.273} & {3} \\ {0.267-0.271} & {1} & {0.274-0.279} & {0}\end{array}$

Answer

NL: v=.00008; std=0.009
AL:v=.00007;std=0.009
variances are very close and the stdevs were approx the same

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Video Transcript

Okay, So for number 26 for us to find the NL vs the A L for I believe it's baseball stuff. So Ah, first things first, we're gonna take thes, frequents these numbers and find the midpoint of um And so when we do that, we add 0.242 plus 0.246 and divide by two. That's going to get us 20.244 0.247 plus 0.251 Divided by two is going to get us 20.2 for nine. And so little to reappoint to five. Uh, point 0.259 point 264 and then point to 69 And then really time for the metric C times the midpoint squared. And then we'll go and do the A l. And then then after that, we will do each very and each state delegation. Okay, so three times 30.24 fours and it goes 0.732 And then when you dio three times point to 4.244 squared and you're gonna be gospel. So I'm going around the three decimal places here. So 30.179 then Ah, 6.249 is 1.494 and then six times 2.249 Square is 0.372 rounded to three decimal places. Ah, one times anything is itself. So point do 54 and then 540.25 squared is going to be ah, 0.65 rounded of times 0.259 is 2.8 for nine and then 11 times 110.259 squared is 0.738 Grounded Island 26 4 is 2.904 and then squared. That midpoint in multiple is 0.767 Lastly, 0.269 and then 0.269 squared times. One is 10.72 were out into the near tent, so go ahead and will add everything up in that column. MP column gets totaled up, wouldn't add up all the rivers you get 8.502 and then when you total those up, you get approximately 2.193 So we'll go and calculate the reinsert Delusional. But we're gonna go ahead and get the midpoint and reached that same process for the Els now. So else we're going to get those mid points. When you do those, you're going to get 0.7395 Next midpoint is 1.51 by 15 at the planet 517 Next midpoint is point to hope. I apologize. I was looking at the wrong column. That's gonna be for later. So those answers are valid. Just not quite. Say it's a 0.2465 then 0.25 25 is the midpoint there, then 0.2585 Next midpoint is 0.2645 Next midpoint is 0.27 05 Then we get 0.2765 All right. Sorry about that before. So now we're gonna go get f times. The midpoint in F comes in one square. That's where those numbers were coming from. My apologies. So now this is where the 10.7395 is seven 395 Then when I do three times 30.246 life's weird And around I'm gonna get point 18 to 3 and then repeat that same process. We at 1.515 and then When it squared, you get 0.38 to 5. Then we get 0.517 than once we square its 0.1336 a 0.2645 And then when we square that's gonna be 0.700 That's going to be 0.8155 And then when we square its 0.2195 and then these will be zero K zero times, anything is zero okay already to total those up each column. So add up the F Times MP column that gets me three point 8475 approximately and then the other. Total it for the last column is approximately 84750.98 79 And so now we're ready to look into our formula to get the variation in the standard deviation. So our end for the NL is 33 so we're going to use that in order to find the variance in the standard deviations of 33 is our end times are last column total 2.193 minus the 8.5 02 squared, divided by 33 times and minus one is 30. Do All right. So we're gonna go ahead and calculate that. And when you do that, you get all right. So when you do all that, you're going to get some very, very, very small numbers here. Okay, So you're going to end up getting, um it's going to give you probably something along the lines of eight 0.4 with some numbers e to the negative five. That's roughly 50.8 rounded and that's our s squared. And then in order to get our s, we square root that number 0.8 And that's gonna get approximately 0.0 nine as an answer, rounded to the nearest three decimal places. So similar story over here, we're going to get very small numbers. And that's because our gland total f times and peace weird was a smaller number than our f times and P column. So that's why we're getting such small numbers here. So no panic. All right, so r n is going to be 15. Here are frequency number. And so that's 15 times 150.9879 minus the three boy eight stuff squared. All that squared all over 15 times 14. Okay, so when we do that, you're going to get approximately another ah e to the negative five. Number 27.2589 e to the negative fits. So that's approximate 0.7 round of the nearest five decimal places as rs squared and then recall that RS is the square root of the 0.7 That's gonna be a practical 0.0 night when you around. So the thing that we can compare here is cause it says toe, discuss the, um results and so compare. The results are variances are very, very close to each other not very far away from each other. But then our sooner deviations are almost the same. So, um, they're batting averages and their stated aviation variances didn't really effect. So even though this had ah higher number than that one, it still came out to be about. Even so, those are different things you can discuss about the problem