Problem

Stem $\qquad$ Leaf 4 $\qquad$ 4 5 6 7 7 5 $\qqu…

12:21

Problem 11 Easy Difficulty

Find the variance and standard deviation of each set of data to the nearest tenth.
{13, 14, 15, 16, 17, 18, 19, 20, 21, 23, 67, 56, 34, 99, 44, 55}

Answer

$\sigma^{2}=569.4$
$\sigma=23.9$

Related Courses

Intro Stats / AP Statistics

Algebra

Algebra 2

Chapter 12

Probability and Statistics

Section 6

Statistical Measures

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Video Transcript

that will always be your first steps. So you look at your list and you count how much you have in your lists. It turns out there's nine. So remember the mean or the average is the same as adding up all of your numbers in your list and then dividing by night. So we're gonna add up the 2.4 plus the 5.6 plus the one 0.9 plus the 7.1 plus the 4.3 plus the 2.7 and 4.6 and the 1.8 and the 2.4 and you get 32.8 already. And then you divide that by nine, and you get 3.6 officially rounds to the nearest 10th of 3.6. So you're going to be using a 3.6 quite often in step two. So very of the seeing how far away your spread is from the mean So, um, we're going to take all the numbers in the list all not above, and subtract the six, the 3.6. So I'm gonna write 2.4, minus 3.6 and 5.613 point six and noticed were squaring because when you subtract, sometimes you're going to end up with negatives. But we can't have negatives were doing very interesting a deviation. So we square that remember whenever you square negative, it becomes positive. So that's why the squaring is going to happen eventually. Sort of subtract first, then square for all nine of these items in the list. So 2.4 minus 3.6 and then we square it get 1.44 Okay, 5.6 minus 3.6. And then I spirit we four. Okay, 1.99 of 3.6 and square it. We get 2.89 7.1. Line 3.6 and square it. You get 12.25 4.3 minus 3.6. Squared is 0.49 2.793 point six squared is pointing one 4.6. Lie in the 3.6 is one. So once weird is one as well. Uh, 1.8 my nephew 0.6. It's negative. 1.8 weeks for that 3.24 and then 2.4 minus 3.6 square is the new one point for four. So the variance officially is the average of all of these numbers that we just calculated. So that means I'm gonna take all nine of these numbers and find the average of so we Adam and divide by nine to get and that will be our variants. So 1.44 plus four was 2.89 plus 12.25 plus point for nine plus 90.81 last one plus 3.24 plus 1.44 Get us 27. 56. Do not turn out nicely. Much weather. Okay. And then we divide that by nine. Okay, so we get 3.1 when we round to the nearest 10th which is what you're gonna probably need to do on some of these. So 3.1 is one of our final answers. But then we take that 3.1, and we use that to get the sinner deviation as our finals at the standard deviation is very simple. You just take the square root of the number that we just got that 3.1 and you scared that and around the near sent, and you should get approximately 1.7. Now, if you square root the whole thing that's from your calculator. It is 1.7. But if you just do the square root of 3.1, then that around a 1.8. So it just depends what you put in your calculator. So I would say, based on the fact that if we're rounding to the nearest 10th here and then we input that into our sin deviation, that's more likely going to work out of your final answer number. Sure, you're a teacher, revealing it with that. It just depends on what they're rounding. Specifications are, so make sure you ask your specific teacher.

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