**STATS MIDTERM NOTES**
Mean
= Xbar =
n
∑
(X
i
/ n)
i
=1
_
Zscore
= Z
i
= X
i
– X
S
Variance
= S^2 =
n
_
∑
(X
i
 X)^2
i
=1
n1
Standard deviation
= sqrt(S^2) = S
Empirical Rule:
In a normal distribution, approx. 2/3 of the sample data are within one standard deviation of the
mean in the interval (Xbar –S, Xbar +S). Approximately 95% of the data are Xbar +/ 2S, and almost all of the
data are Xbar +/ 3S.
To correctly describe a single quantitative variable
:
Center
(Where is most of the data located? (If we had to pick
one number, what would be the best representative?)),
Spread
(Over what range do we see most of the data? How
good is our representation?),
Skew
(positive (right), negative (left), symmetric) (What direction does the spread
extend to?),
Weird things
(outliers, multiple modes)(Are some points really far away? Do we have two centers?)
Dot plot:
easy to see all data points and to interpret, but gets messy and loses the big picture
Measures of Central Tendency:
the tendency of the data to cluster about certain numerical values; mean, median
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 Fall '08
 Dr.JoseCorrea
 Statistics, Empirical Rule, Normal Distribution, Standard Deviation, Variance, Probability theory, Ac Bc Dc, n1 Standard deviation

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