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# Which of the following statements best describes

## Tags: Mathematik

23:12 Uhr, 03.08.2022

Tag, dear supporters and helpers
I am having trouble doing this excersie. can you guide me to a solution?
thanks for any tips

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00:51 Uhr, 04.08.2022

Hello,

It seems that there are different measures of spreads, i.e. Range, interquartile range, and standard deviation (variance). In the case of variannce you should know that an added constant $c\phantom{\rule{0.12em}{0ex}}$ does not change the variance: $v\phantom{\rule{0.12em}{0ex}}a\phantom{\rule{0.12em}{0ex}}r\phantom{\rule{0.12em}{0ex}}\left(x\phantom{\rule{0.12em}{0ex}}+c\phantom{\rule{0.12em}{0ex}}\right)=v\phantom{\rule{0.12em}{0ex}}a\phantom{\rule{0.12em}{0ex}}r\phantom{\rule{0.12em}{0ex}}\left(x\phantom{\rule{0.12em}{0ex}}\right)$.

Check a smaller example. The data set 1 is 1,2,3. What is the variance here?

Now add 1 to every value. Data Set 2 then is 2,3,4. What is the variance for the set?

greetings,
pivot

01:58 Uhr, 04.08.2022

Pivot what about if $i\phantom{\rule{0.12em}{0ex}}$ do this way, would it be correct?

write out all data points given
it starts at $30,000,40,000,50000,60000$

then $i\phantom{\rule{0.12em}{0ex}}$ find the mean by the old fashioned way
sum of all data points / number of data points in the set= that gives me $45,000$

then the median of this data set is $45,000$.

if $i\phantom{\rule{0.12em}{0ex}}$ add $1000$ to every data point, the mean changes to $46,000$
and the median is $46,000$
so the mean and the median does not change. they remain the same.
Is this correct?
to find the variance or standard deviation I can use the formula for that, where
$\sigma \phantom{\rule{0.12em}{0ex}}$ =population standard deviation
$N\phantom{\rule{0.12em}{0ex}}=$the size of the population
${x\phantom{\rule{0.12em}{0ex}}}_{i\phantom{\rule{0.12em}{0ex}}}=$each value from the population
$u\phantom{\rule{0.12em}{0ex}}=$the population mean

do you agree?

02:15 Uhr, 04.08.2022

I agree to the first part, although I don't how it is related to the question.

To find the variance of the sets you can use the formula for the standard deviation/variance.

03:05 Uhr, 04.08.2022

okay, thank you pivot.

15:14 Uhr, 04.08.2022

Tag,
Wie kann ich in La Tex die Formel für die Standardabweichung eingeben?

16:28 Uhr, 04.08.2022

You can copy it more or less from wiki:

de.wikipedia.org/w/index.php?title=Empirische_Varianz&action=edit§ion=2

You copy the formula

\sigma^2= \frac{1}{N} \sum _{i=1}^N(x_i-\mu)^2

Then put the formula in between two dollar signs $\phantom{\rule{0.167em}{0ex}}$ to obtain

${\sigma \phantom{\rule{0.12em}{0ex}}}^{2}=\frac{1}{N\phantom{\rule{0.12em}{0ex}}}\sum _{i\phantom{\rule{0.12em}{0ex}}=1}^{N\phantom{\rule{0.12em}{0ex}}}\left({x\phantom{\rule{0.12em}{0ex}}}_{i\phantom{\rule{0.12em}{0ex}}}-\mu \phantom{\rule{0.12em}{0ex}}{\right)}^{2}$

17:33 Uhr, 04.08.2022

Vielen Dank!

17:35 Uhr, 04.08.2022

Gerne.