can a unit be associated with the mean and standard deviation values or these are "dimensionless" quantities?

For instance, if I am computing distance, with unit being meters (m), and I have got the following values:

Min: 11 (m)

Max: 18 (m)

Mean: 14.5 (m)

Standard deviation: 1.5 (m)

Can we use "m" with mean and standard deviation to express unit of distance?


Mean and standard deviation have dimensions, the same ones from your data. Take your example: $$ \text{mean distance } d \; [\text{in}\; m] = \mathbb{E}( d \; [\text{in}\; m]) = \cfrac{1}{n} \sum\limits_{j = 1}^{n} d_j \; [\text{in} \; m] = \mu \; [\text{in}\; m] $$

$$ \begin{aligned} \text{variance of distance } d \; [\text{in}\; m] &= \mathbb{E}(\, (d \; [\text{in}\; m] - \mu \; [\text{in}\; m])^2\,) \\ &= \cfrac{1}{n} \sum\limits_{j = 1}^{n} (d_j - \mu \; [\text{in} \; m] )^2 = \sigma^2 \; [\text{in}\; m^2] \\ &\Rightarrow \text{standard deviation } = \sqrt{\sigma^2 \; [\text{in}\; m^2]} = \sigma \; [\text{in}\; m] \end{aligned}$$

(for simplicity I've assumed that all distances in your dataset follow a uniform probability)


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.