# Student’s t-distribution

**Student’s t-distribution** is a continuous probability distribution commonly used in statistics.

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The t-distribution is a type of normal distribution(are we sure that’s right??) used with small sample sizes where the population standard deviation/population variance is unknown. Its mean is 0, and its skewness is 0 (i.e. it is symmetrical). The shape of the distribution depends on its standard deviation, which is estimated from the degrees of freedom, which is taken as the number of observations -1. The t-distribution has slightly higher kurtosis than the normal distribution, i.e. it is thinner in the middle and fatter in the tail.

As the sample size increases, the t-distribution comes closer to the normal distribution because of the central limit theorem, and for sample sizes of >30 a z-distribution can be used instead.

The t-distribution is the basis for the t-test series of tests.

The distribution takes the name of the statistician Student (W.S. Gosset), who originated it.

The spreadsheet function `TDIST()`

can be used to generate this distribution.

Without the use of statistical computing, the t-table gives the distribution for each degree of freedom.

There are two types; 1-tailed t-distribution and 2-tailed t-distribution.