from what i have gathered . I know that pivots are functions that give approximate or exact assumption of CI . I'm not entirely sure what is the quantity the question is referring to.
does the quantity mean the mean, standard deviation etc.?
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$\begingroup$A pivotal quantity for a parametrized family of probability distributions is a random variable, usually (or maybe always) depending on one or more of the unobservable parameters, whose probability distribution does not depend on the vaues of any of the observable parameters.
Thus if $$ X_1, \ldots, X_n\sim\mathrm{i.i.d.}\ N(\mu,\sigma^2) $$ then $\mu$ and $\sigma^2$ are the unobservables and $$ \frac{\bar X-\mu}{\sigma/\sqrt{n}} $$ is a pivotal quantity, where $\bar X=(X_1+\cdots+X_n)/n$, because its distribution $N(0,1)$, does not depend on $\mu$ or $\sigma^2$.
Also $$ \frac{\bar X - \mu}{S/\sqrt{n}} $$ with $\bar X$ as above and $S^2 = ((X_1-\bar X)^2+\cdots+(X_n-\bar X)^2)/(n-1)$, is a pivotal quantity, since its distribution, $t_{n-1}$, does not depend on $\mu$ or $\sigma^2$.
Notice that the values of these two pivotal quantities are not observable, since both depend on $\mu$ and one of them depends on $\sigma^2$. That means neither of them is a statistic.
Knowing the distribution of the first pivotal quantity above makes it possible to find a confidence interval for $\mu$ if $\sigma$ is known (not realistic). Knowing the distribution of the second pivotal quantity above makes it possible to find a confidence interval for $\mu$ in realistic situations, and it is used incessantly.
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