Download Worksheet #2

WORKSHEET #2
STA 291
Summer 2010
Summarizing Data
Mean: arithmetical average
Median: middle value
Mode: most frequently occurring value
Minimum: smallest value
Maximum: largest value
Variance:
Population

2
 (x  )

i
N
Sample
2
s
2
 ( x  x)

i
2
n 1
Standard Deviation: square root of the variance (σ, s)
Empirical Rule
Suppose the distribution of a set of data is bell-shaped (or normal).
 ____% of the data values fall within one standard deviation of the mean.
 ____% of the data values fall within two standard deviations of the mean.
 ____% of the data values fall within three standard deviations of the
mean.
Examples
Suppose that the scores on a national achievement exam have a mean of 200
and a standard deviation of 40. If these scores are normally distributed.
Approximately 68% will fall between ____ and ____.
Approximately 95% of the scores will fall between ____ and ____.
Approximately 99.7% of the scores will fall between ____ and ____.
Sample:
13
20
𝑥̅ =
s2 =
s=
Median =
Mode =
Minimum =
Maximum =
Range =
13
21
16
24
17
27
18
31