Question

how to calculate sample variance, Vs^2

Answer 1

\[s^{2} = \frac{\sum_{}^{}(x_{i}-u)^{2}}{n-1}\]
u is mean of sample
n is number of items in sample
x_i is value of each item in sample

Answer 2

what does sample variance tell us?

Answer 3

basically how spread out the data is...higher variance means larger gaps between data points in sample

Answer 4

xi is value of each item, so if we have many values for the items we have to that it and subtract with u square it and add them up?

Answer 5

how is it different from standard deviation?

Answer 6

yes, you have to add each squared difference
if they are a lot of items its best to use software like excel to add everything up

Answer 7

standard deviation is just the square root of variance and is used more often, it tells us how far away an average item is from the mean

Answer 8

lets say i have numbers 35, 42,38,55,70,69 and i want to calculate the population variance..

Answer 9

how do i use the formula

Answer 10

there are 6 items...n=6
find the mean(avg) by adding them up and dividing by 6...this gives you u
then sum up
(35-u)^2
(42-u)^2
...
and so on

Answer 11

what if we are given \[\sum_{?}^{?}(X i -c)\]

Answer 12

c is constant, then how to calculate sample variance

Answer 13

why is the constant there and what does it mean

Answer 14

i dont know
it seems like you are just adding up all the items in the sample

Answer 15

after subtracting a constant from each one

Answer 16

and what is unbiased estimator?

Answer 17

its a value computed from a sample that truly represents the population or if you took a bunch of samples then the mean would equal the population value.
mean is an unbiased estimator
so is standard deviation
however, variance is not

Answer 18

omg why are there so many confusing terms how do i understand them

Answer 19

first of all i have a population so i am actually drawing a sample

Answer 20

so when i draw a sample it's a representative of the population?

Answer 21

yes correct as long as the sample is random or unbiased

Answer 22

so this sample, i will have to calculate all the parameters to see what the sample is like?
and those include mean and variance

Answer 23

so since it is a sample it's not the same as the population so they're given different terms like sample variance, sample mean?

Answer 24

yes
we use samples because many things have very large populations and it is impossible to get data on everything

right, however if it is a large enough sample and is random we can treat the sample data like mean and standard deviation as though it represents the whole population,

Answer 25

yes i agree so if the sample is very large and just like the population we're using unbiased estimators?

Answer 26

i believe so

Answer 27

so this unbiased thing is the most accurate we can say?

Answer 28

yeah
basically just understand how to compute the sample mean, variance and such and understand it is an approximation of the population. thats all you really need to know

Answer 29

is statistics all about calculation of erm... a sample.. getting their characteristics and all since a population is too big?

Answer 30

yeah pretty much
everything is samples and inferring that onto the population
population mean and variance is just theoretical not really practical

Answer 31

and there're formula for unbiased estimators too!

Answer 32

so with every statistic there is a margin of error, though usually very small

Answer 33

how do i remember they all look so symboly to be

Answer 34

formula for unbiased estimator ??? not sure
which one, mean or standard deviation

Answer 35

dont worry too much about term unbiased estimator, its just used to classify different measures of sample data

Answer 36

it says mule = small x bar (unbiased estimate for mean) that means we dont have to calculate?
then unbiased estimate for variance= n/(n-1)vs^2

Answer 37

you will use mean, variance, median, standard variance much more often

Answer 38

no it just means x bar is an unbiased estimate, but all you have to do is calculate the average of the sample data

Answer 39

what does "v" mean in vs^2 ??

Answer 40

hmmm i'll digest all these information slowly...... i think knowing all these are useful for hypothesis testing is it?

Answer 41

it's sample variance

Answer 42

oh ok
yes knowing this is helpful for hypothesis testing

Answer 43

for hypothesis tests, usually have to find mean and standard deviation of sample