Transcript Example(cont.)

Measures of
Center and Variation
Sample mean
Example: The birth weights in pounds: 9.2, 6.4, 10.5, 8.1, 7.8.
The mean is (9.2 + 6.4 + 10.5 + 8.1 + 7.8) / 5 = 8.4
Figure 2.9 (p. 42)
Dot diagram and the sample mean for the birth-weight data.
Sample median
Example(cont.): The birth weights in pounds: 9.2, 6.4, 10.5, 8.1, 7.8.
The median is 8.1 .
Note: The median is not affected by a few very small or very large
observations, whereas the presence of such extremes can have a
considerable effect on the mean.
The sample 100 p-th percentile is a value such that after the data
are ordered from smallest to largest, at least 100p % of the
observations are at or below this value and at least 100(1-p) % are
at or above this value.
An example of percentiles
To determine the first quartile
• take p=.25
• 38 * .25 = 9.5
• round 9.5 up to 10
• 10th ordered observation is 4.4
• so the first quartile is Q1 = 4.4
Figure 2.10 (p. 49)
Dot diagrams with similar center values but different amounts of variation.
Box on Page 50
Sample variance of n observations
Table 2.10 (p. 50)
Calculation of Variance
To obtain a measure of variability in the same unit as the data, take
the positive square root of the variance:
Box on Page 51
Sample Standard Deviation
Other measures of variation
Example of phone calls (table 8): Sample range = 53.3 – 1.6 = 51.7
Note: sample range is very sensitive to the existence of a very large
or very small observation in the data set.
Example of phone calls: Sample interquartile range = 17.5 – 4.4 = 13.1
Boxplots
• The center half of the data, from the first to the third
quartile, is represented by a rectangle (box) with the median
indicated by a bar.
• A line extends from Q3 to the maximum value and another
from Q1 to the minimum.
Figure 2.12 (p. 55)
Boxplot of the length of phone call data in Table 8