Tip:
Highlight text to annotate it
X
So we have eight male students weights in pounds, recorded here, and we're going to
find the standard deviations of these weights.
and just to be clear, this data was a sampling, and so we're going to use the
sample standard deviation here. So the first thing we need to do is find,
is find the mean of our data. And so to do that, we'll go ahead and
just add up all of our data. so when we add up all of our data here,
which adds up to 1400. and divide it by the number of data
values. We got eight data values.
and we end up with a mean of 175. So now we can take each value take each
value and find our deviation from the mean so for the weight of 165 the
deviation would be, that's not the right number.
It should be the mean. minus 175 is negative 10, is our
deviation there. For 145, we got 145 minus 175 is negative
30. for 160, we got negative 15.
and so on for the rest of the values. So now that we have all the deviations
calculated, now we can go and find our squared deviations.
So we're going to do that by squaring each of these values.
So negative 10 squared is 100. Negative 30 squared is 900.
15 squared is 225. 25 squared is 625.
Negative 25 squared but when we square it, it becomes negative, sorry, becomes
positive. 5 squared is 25.
45 squared is 2045. 25 squared is 625, and 5 squared is 25.
and now we'll go ahead and add all those up and the sum of all of our deviations
is 45-uh-50. So remember that's standard deviation is
found by finding the sum of the square deviations, and then dividing by either n
or n minus 1. N if it's from the population or n minus
1, if it's from the sample. So we're going to take our sum of, of, of
squared deviations here. And because this is from a sample, we're
going to divide by n minus 1. So we're going to take our 4550 and
divide it by. 7, which is one less than our number of
data which was eight pieces of data. So we go ahead and divide that and we end
up with 650, again that's what we call variance, and then our standard
deviation, standard deviation will be the square root of that variance.
So the square root of 650 is about 25.5. It's actually, like, 25.4951.
but, again, typically, we round to 1 more decimal place than our original data had.
And so our standard deviation is 25.5 pounds.
Standard deviation is measured in the same units as the original data.
so there is the standard deviation.