- published: 01 Feb 2013
- views: 156165
In probability theory and statistics, the variance is a measure of how far a set of numbers is spread out. It is one of several descriptors of a probability distribution, describing how far the numbers lie from the mean (expected value). In particular, the variance is one of the moments of a distribution. In that context, it forms part of a systematic approach to distinguishing between probability distributions. While other such approaches have been developed, those based on moments are advantageous in terms of mathematical and computational simplicity.
The variance is a parameter describing in part either the actual probability distribution of an observed population of numbers, or the theoretical probability distribution of a sample (a not-fully-observed population) of numbers. In the latter case a sample of data from such a distribution can be used to construct an estimate of its variance: in the simplest cases this estimate can be the sample variance, defined below.
The variance of a random variable or distribution is the expectation, or mean, of the squared deviation of that variable from its expected value or mean. Thus the variance is a measure of the amount of variation of the values of that variable, taking account of all possible values and their probabilities or weightings (not just the extremes which give the range).
(VERSE 1)
Now stop me if you've heard this one before
And I promise I'll change my tune
But if not, I'll sing you to sleep like a songbird
And swear on my feathers it's true
So draw the shades and close your eyes
And put on your sunglasses too
Cause where we're going
The sun's still glowing
And your eyes can't adjust to all of this new
(PRE-CHORUS)
So hush, be quiet, let me speak
No, this can't wait until next week so
(CHORUS)
Hey, are you ready for this?
It's 5th finger promise, sealed with a kiss
I'm an open book,
I'm a silhouette
I'm a shade of what I used to be
So tell me once, tell me twice, and tell me again
"You and I, we were made for this"
Turn to chapter you,
And you will find chapter me
(VERSE 2)
I'm hoping these words ring true
Cause I would save my words for you
And then listen to your breathing
As we both stared at the ceiling, thinking
"Wouldn't it be great
If all the ghosts that haunted us
Stopped til daybreak?"
Cause I'm tired, oh so tired...
(PRE-CHORUS)
So hush, be quiet, let me speak
No, this can't wait until next week so
So hush, be quiet, let me speak
No, this can't wait until
(CHORUS)
Hey, are you ready for this?
It's 5th finger promise, sealed with a kiss
I'm an open book,
I'm a silhouette
I'm a shade of what I used to be
So tell me once, tell me twice, and tell me again
"You and I, we were made for this"
Turn to chapter you,
And you will find chapter me
(BRIDGE)
So on this fateful prom night
We won't have to dance in my garage
I spent 15 minutes with you
And spent the whole night thanking God
So lets ditch this after-party
And make one of our own
Just give me half an hour
And we can both be gone.
(CHORUS)
Hey, are you ready for this?
It's 5th finger promise, sealed with a kiss
I'm an open book,
I'm a silhouette
I'm a shade of what I used to be
So tell me once, tell me twice, and tell me again
"You and I, we were made for this"
Turn to chapter you,