# Download 6.1B Notes File - Northwest ISD Moodle

Survey
Was this document useful for you?
Thank you for your participation!

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Document related concepts

History of statistics wikipedia, lookup

Statistics wikipedia, lookup

Randomness wikipedia, lookup

Probability wikipedia, lookup

Probability interpretations wikipedia, lookup

Transcript
```AP Statistics
6.1B Notes
Standard Deviation (and Variance) of a Discrete Random Variable
The variance of a random variable is an average of the squared deviation  xi   x  of the values of the
2
variable X from its mean  x . To get the standard deviation of a random variable, we take the square root of
the variance. The standard deviation of a random variable X is a measure of how much the values of the
variable tend to vary, on average, from the mean  x .
Suppose that X is a discrete random variable whose probability distribution is
Value:
…
x1
x2
x3
Probability:
p1
p2
p3
…
and that  x is the mean of X. the variance of X is
Var(X)   x2   x1   x  p1   x2   x  p2   x3   x  p3  ...
2
2
2
=  xi   x  pi
2
The standard deviation of X,  x is the square root of the variance.
Example
A large auto dealership keeps track of sales made during each hour of the day. Let X = the number of cars sold
during the first hour of business on a randomly selected Friday. Based on previous records, the probability
distribution of X is as follows:
Cars sold
0
1
2
3
Probability
0.3
0.4
0.2
0.1
1. Compute and interpret the mean of X.
2. Compute and interpret the standard deviation of X.
Continuous Random Variables
A continuous random variable X takes all values in an interval of numbers. The probability distribution of X is
described by a density curve. The probability of any event is the area under the density curve and above the
values of X that make up the event.
The probability distribution for a continuous random variable assigns probabilities to intervals of outcomes
rather than to individual outcomes. In fact, all continuous probability models assign probability 0 to every
individual outcome. Only intervals of values have positive probability.
```