Question

Within how many standard deviations of the mean doe the values fall?

Answer 1

16, 19, 25, 32, 38, 40

Answer 2

@phi

Answer 3

I assume we use the mean and std from the previous question ?

Answer 4

no, it's a completely different question... those were on a line graph.. I just gave the points that were plotted.

Answer 5

we need the mean and std of these numbers to answer the question

Answer 6

okay.. so the mean is 28.3333..

Answer 7

right?

Answer 8

can you post the exact question, with the graph ?

Answer 9

yes, the mean is 28.333

Answer 10

I am wondering if they really want you to find the mean and std first, or if the info is given in the question.

but to find the std, we do
x - mean
for each of the 6 numbers
square each number
find the average (this will be the variance)
take the square root to find the std deviation

now we do
(x - mean)/std for each number to answer the question

Answer 11

sorry it took so long.. OS locked up for me

Answer 12

ok, it sounds like we find the mean and std.
we got the mean
can you find the std ? (see above for the process)

Answer 13

256+361+625+1024+1444+1600=5300
5300/6=883.3333..

Answer 14

how did you get 256 for the first number ?

Answer 15

you must have done 16*16 ?

you want to do (x - mean)^2 not x^2

Answer 16

the idea is to "measure" how far away each x is from the middle x (the mean)
so we do x-mean
then people decided it's better to square the number before finding the average...
to get the variance

Answer 17

ohhhhhhhhh

Answer 18

so it's be 16-28.333 then square the difference?

Answer 19

yes: difference, square,
then find the average of those

Answer 20

oh my.. why is it so complicated? >.<

Answer 21

Yes, it is a bit of a pain (though computers do most of the work these days)
the amazing thing is the real world can be analyzed using these ideas (though it's not amazing until after you learn this stuff and start using it, and then thinking about *how* can this work.)

Answer 22

152.1+87.1+11.1+13.45+93.45+136.12=493.41
493.41/6=82.235

Answer 23

ok, that is the variance
last step is find the standard deviation

Answer 24

how do we do that?

Answer 25

variance = \(\sigma^2\)
or
\[ \sigma= \sqrt{variance} \]

Answer 26

we want sigma (greek letter s, short for standard deviation)

Answer 27

the std dev is sqrt(82.235)

Answer 28

9.06?... that's not an option

Answer 29

now we measure how far the lowest number is from the mean, but not by just doing subtraction. First we do the subtraction:
16-28.33 = -12.33
next (and this is the interesting idea), we ask how many "deviations" away are we
in other words, divide this by 9.06: -1.36
that says 16 is -1.36 standard deviations away from the mean. (negative means below the mean)

Answer 30

now do the upper limit
40 is 40-28.33 = 11.67 units above the mean
but in "standard deviations" (i.e. how many "std" away is it from the mean) it is
11.67/9.06 = 1.29 standard deviations above the mean

so the answer is roughly \(\pm 1.4 \)