Download FORMULA SHEET NUMBER ONE (consists of 2 pages)

FORMULA SHEET NUMBER ONE (consists of 2 pages)
DESCRIPTIVE STATISTICS
SAMPLE MEAN
x=
x
n
SAMPLE VARIANCE (variance OF the sample)
 x2
svar =
-x
n
2
“The mean of the squares less the square of the mean.”
Also known as "MSD," -- Mean of the Squared Deviations.
(A deviation is the difference between a data item and the mean.) The
formula below also computes MSD and, if calculated carefully, gives
exactly the same result as the formula above. The first formula,
however, tends to be more efficient and easier to compute, especially
if n is large.
 (x - x )2
svar = MSD =
n
SAMPLE STANDARD DEVIATION (std. dev. OF the sample)
ssd =
svar
This is the smaller of the two standard deviations provided by the TI 83/84.
INFERENTIAL STATISTICS
ESTIMATE OF POPULATION MEAN
̂ = x
The sample mean is an unbiased estimator of the population mean.
ESTIMATE OF POPULATION VARIANCE
n
)
ˆ = (svar)(
n -1
2
The sample variance is a biased estimator of the population variance. The
bias is due to the probable absence of outliers in the sample. n / (n-1)
corrects (removes) the bias.
The text refers to this as "s2," and "sample variance." But note that this is
not the variance of the sample. It is called sample variance because it was
calculated from the sample.
ESTIMATE OF POPULATION STANDARD DEVIATION
ˆ = ˆ 2 = ssd
n
n -1
The sample standard deviation is a biased estimator of the
population standard deviation. The text refers to this as "s," and "sample
standard deviation." But note that this is not the standard deviation of the
sample. It is called sample standard deviation because it was calculated
from the sample.
This is the larger of the two standard deviations provided by the TI 83/84.