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I am reading about t-distributions in a rather non-rigorous book.

An example is given here where the sample size is 25. The example also gives a numerical table used to determine the probability of getting a given numerical t-value $ t \geq x $ by chance.

But the example says that to determine this probability, we should look at the table row which says 24 degrees of freedom and not 25. Is that a typo or actually a rule i.e. when the sample size is 25 how many are the degrees of freedom? Also why are they named this way?

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More context to your question would help, but anyway:

1) Is that a typo or actually a rule i.e. when the sample size is 25 how many are the degrees of freedom?

It is probably not a typo. I can guess that you are talking about $t$-test for $\mu$ in a statistical Normal model/distribution with unknown variance $\sigma^2$. Where the distribution of the statistic $\frac{\bar{x}_n - \mu}{s/\sqrt{n}}$ is $t$ with $n-1$ degrees of freedom. So, for $n=25$ it is indeed $t^{(24)}$.

2) Also why are they named this way?

Intuitively, you are estimating $\mu$ by the sample mean $\bar{x}_n$, so you setting the sum $\sum_{i=1}^nx_i$ to equal some value $c$, as such you have $n-1$ elements to choose freely while the last term is constraint to equal $c-\sum_{i=1}^{n-1}x_i$. So, you have $n-1$ df.

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