# tfp.substrates.numpy.stats.stddev

Estimate standard deviation using samples.

Given `N` samples of scalar valued random variable `X`, standard deviation may be estimated as

``````Stddev[X] := Sqrt[Var[X]],
Var[X] := N^{-1} sum_{n=1}^N (X_n - Xbar) Conj{(X_n - Xbar)},
Xbar := N^{-1} sum_{n=1}^N X_n
``````
``````x = tf.random.stateless_normal(shape=(100, 2, 3))

# stddev[i, j] is the sample standard deviation of the (i, j) batch member.
stddev = tfp.stats.stddev(x, sample_axis=0)
``````

Scaling a unit normal by a standard deviation produces normal samples with that standard deviation.

``````observed_data = read_data_samples(...)
stddev = tfp.stats.stddev(observed_data)

# Make fake_data with the same standard deviation as observed_data.
fake_data = stddev * tf.random.stateless_normal(shape=(100,))
``````

Notice we divide by `N` (the numpy default), which does not create `NaN` when `N = 1`, but is slightly biased.

`x` A numeric `Tensor` holding samples.
`sample_axis` Scalar or vector `Tensor` designating axis holding samples, or `None` (meaning all axis hold samples). Default value: `0` (leftmost dimension).
`keepdims` Boolean. Whether to keep the sample axis as singletons.
`name` Python `str` name prefixed to Ops created by this function. Default value: `None` (i.e., `'stddev'`).

`stddev` A `Tensor` of same `dtype` as the `x`, and rank equal to `rank(x) - len(sample_axis)`

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