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WORKSHEET #3
STA 291 (022-024)
1/30/08
Summarizing Data
Mean: arithmetical average
Median: middle value
Mode: most frequently occurring value
Minimum: smallest value
Maximum: largest value
Variance:
Population

2
 (x  )

i
Sample
2
N
s
2
 ( x  x)

i
2
n 1
Standard Deviation: square root of the variance (σ, s)
Percentiles
The pth percentile of data set is a value Xp such that p% of the data are below Xp.
X25 = Q1 = lower quartile
X50 = Q2 = median
X75 = Q3 = upper quartile
Examples
5 students were asked to predict their scores on a midterm exam. Their
predictions were as follows:
50
80
70
40
60
=
s2 =
s=
Data set:
13
20
13
21
16
24
17
27
18
31
Mean =
Median =
Mode =
Minimum =
Maximum =
Q1 =
Q3 =
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.
Example
Suppose that the scores on a national achievement exam have a mean of 480
and a standard deviation of 90. If these scores are normally distributed, then
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 ____.