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Problem 23 Hard Difficulty

The tables below give the distribution of high
temperatures in degrees Fahribution of for City $\mathrm{A}$
and City $\mathrm{B}$ over the same 21 days in March.
Which of the following is true about the data shown
for these 21 days?
A) The standard deviation of temperatures in
City $\mathrm{A}$ is larger.
B) The standard deviation of temperatures in
City B is larger.
C) The standard deviation of temperatures in these
D) The standard deviation of temperatures in these
cities cannot be calculated with the data
$\quad$ provided.

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Video Transcript

Okay, So if you look at the the answer choices, we know that we're comparing the standard deviations. So let's think about what standard deviation even is. Well, standard deviation is just a measure at the spread of the data. So we're trying to see is it very spread out? Which means it has a big, tentative Asian or is it pretty? Is the data pretty like clump together towards one and or like what? A certain point, Which means it has a small sanity patient. So for this one, we can see that for a almost all the points are calculated towards the seventeen ninety two point, whereas like there's not very much towards the ends. So we know that the onus probably could have a pretty small standard deviation, whereas for the city be that one is just all over the place. It's got data points at so many different places, so we know that that was going to have a pretty big standard deviation because its spread is very spread up. And if you want to think about another way to get it, think about, would it be easy to predict where what temperature might come next like, for example, if I had one choice one, I guess I would probably guess that the standard for city A tomorrow is going to be seventy nine degrees because it's so much more often that seven nine degrees, whereas for City be, I probably would not really know what to guess, but when maybe go a seventy six or eight e. But again, it's hard because the Senate donations so big, meaning it's hard to guess or project. So let's look at it. Hey, says the city. A standard deviation ist bigger, which we've already said it's not. The Senate invasion of temperature in City B is larger. Sobhi is correct because, yeah, it is larger. We just at that.