Clarify the difference between mu and xbar in the statistics documentation

[stevendaprano]

BPO	36099
Nosy	@rhettinger, @stevendaprano, @applio, @csabella
Superseder	bpo-20389: clarify meaning of xbar and mu in pvariance/variance of statistics module

^{Note: these values reflect the state of the issue at the time it was migrated and might not reflect the current state.}

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GitHub fields:

assignee = 'https://github.com/csabella'
closed_at = <Date 2021-08-20.10:12:22.222>
created_at = <Date 2019-02-24.03:39:59.904>
labels = ['type-bug', '3.8', 'docs']
title = 'Clarify the difference between mu and xbar in the statistics documentation'
updated_at = <Date 2021-08-20.10:12:22.222>
user = 'https://github.com/stevendaprano'

bugs.python.org fields:

activity = <Date 2021-08-20.10:12:22.222>
actor = 'iritkatriel'
assignee = 'cheryl.sabella'
closed = True
closed_date = <Date 2021-08-20.10:12:22.222>
closer = 'iritkatriel'
components = ['Documentation']
creation = <Date 2019-02-24.03:39:59.904>
creator = 'steven.daprano'
dependencies = []
files = []
hgrepos = []
issue_num = 36099
keywords = []
message_count = 5.0
messages = ['336424', '336434', '336438', '336447', '336463']
nosy_count = 5.0
nosy_names = ['rhettinger', 'steven.daprano', 'docs@python', 'davin', 'cheryl.sabella']
pr_nums = []
priority = 'normal'
resolution = 'duplicate'
stage = 'resolved'
status = 'closed'
superseder = '20389'
type = 'behavior'
url = 'https://bugs.python.org/issue36099'
versions = ['Python 3.8']

[stevendaprano]

The documentation isn't clear as to the difference between mu and xbar, and why one is used in variance and the other in pvariance.

See bpo-36018 for discussion.

For the record: mu or μ is the population parameter, i.e. the mean of the entire population, if you could average every individual. xbar or x̅ is the mean of a sample.

[applio]

Without necessarily defining what each means, perhaps it is sufficient to change this clause in the docs:
it should be the mean of data

For pvariance() it could read as:
it should be the *population* mean of data

And for variance() it could read as:
it should be the *sample* mean of data

[rhettinger]

Without necessarily defining what each means,
perhaps it is sufficient to change this clause in the docs

+1 That is a simple way to address the concern.

[stevendaprano]

I'm happy with that doc change.

If nobody objects, this might make an easy "Good first issue" for the upcoming sprint. Assigning to Cheryl to stop anyone else grabbing it.

[csabella]

Great! Thank you, Steven.