What is a pooled variance?

Answer 1

#((n_1-1)s_1^2+(n_2-1)s_2^2)/(n_1+n_2-2)#

Let consider we have two sets of data with #n_1# and #n_2# size. Also consider their variances as #s_1^2# and #s_2^2#. Then pooled variance means the variance of combined data sets with size #n_1+n_2# and it is defined as

#((n_1-1)s_1^2+(n_2-1)s_2^2)/(n_1+n_2-2)#

You can combine more than two data sets also. If you have data sets with sizes #n_1, n_2 .... n_k# and variances #s_1^2, s_2^2 .... s_k^2# then pooled variance is defined as

#((n_1-1)s_1^2+(n_2-1)s_2^2+...+(n_k-1)s_k^2)/(n_1+n_2+...+n_k-k)#

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Answer 2

Dominic Amato

Pooled variance refers to a method used in statistics to combine the variances of two or more samples into a single estimate of variance. It is often used in situations where the samples are drawn from populations with similar variances. This method takes into account both the size of each sample and the variability within each sample when calculating the overall variance.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.