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Home , Deviation (statistics), Standard deviation, Variance

Section 8.3 and Standard

Variance of a Random X Suppose a has the

x x1 x2 ... xn

P (X = x) p1 p2 ... pn and (or )

E(X)=µ (pronounced“mu”)

Then the variance of the random variable X is

V ar(X)=p (x µ)2 + p (x µ)2 + ...+ p (x µ)2 1 1 2 2 n n The variance is one measure of the spread of a probability distribution about its mean.

Standard Deviation of a Random Variable X The of a random variable X denoted (pronounced “”), is defined by

= V ar(X) p Calculator Steps

STAT ,EDIT, ENTER . Enter the random variable values into L1 and the probabili-

ties/frequencies into L2 .

STAT , CALC ,1.Youshouldsee1-VarStats on the screen. Then click 2ND ,1,,, 2ND , 2 , ENTER .

x is the standard deviation and if you that value, (x)2, you will get the variance. Also, as mentioned in last class,x ¯ is the mean or expected value.

1. The probability distribution of a random variable X is given.

x 410 490 530 P (X = x) .2 .5 .3

Find the mean, standard deviation, and variance of X. (Round answers to two decimal places.) 2. Find the variance of the probability distribution for the shown. (Round answer to two decimal places.)

3. The following table gives the math SAT scores for males and females in the past five years. Find the mean, standard deviation, and variance for each group. (Round answers to two decimal places.)

Males 504 505 503 496 500 Females 454 452 450 451 447

Which group is varying more?

2 Spring 2017, Maya Johnson 4. The distribution of the number of chocolate chips (x)inacookieisshowninthefollowingtable.

x 0 1 2 3 4 5 6 7 8 P (X = x) .01 .04 .05 .11 .12 .24 .22 .17 .04

Find the mean and the variance of the number of chocolate chips in a cookie. (Round answers to two decimal places.) 4.98¥ 7@

5. An consists of rolling a pair of fair 4-sided dice and observing the sum of the uppermost numbers. Find the mean and the variance of the experiment. %

mean

1 58 =5?- . ? ✓ar(X)= ( 1.58 ) = 2.5€

3 Spring 2017, Maya Johnson