The formulas for the sample mean and the population mean only differ in mathematical notation.. Most values cluster around a central region, with values tapering off as they go further away from the center.. If the p-value so observed is not less than the significance level α, then theoretically null hypothesis is accepted.

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3% (less than 5%), which eventually means that we will eliminate our null hypothesis and will accept an alternative hypothesis. This can happen when calculating the mean value

y

Continue avg

{\displaystyle y_{\text{avg}}}

of a function

f
(
x
)

{\displaystyle f(x)}

. It is defined for a set of n positive numbers xi by

x

(
m
)
=

(

1
n

read here i
=
1

n

x

i

m

)

1
m

{\displaystyle {\bar {x}}(m)=\left({\frac {1}{n}}\sum _{i=1}^{n}x_{i}^{m}\right)^{\frac {1}{m}}}

2
By choosing different values for the parameter m, the following types of means are obtained:
This can be generalized further as the generalized f-mean
and again a suitable choice of an invertible f will give
The weighted arithmetic mean (or weighted average) is used if one wants to combine average values from different sized samples of the same population:
Where

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x

i

{\displaystyle {\bar {x_{i}}}}

and

w

i

{\displaystyle w_{i}}

are the mean and size of sample

i

{\displaystyle i}

respectively..

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