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Chapter 1.2
Describing Distributions with Numbers
Measuring Center
 Mean:
◦ Arithmetic average
◦ Denoted
x
◦ Non-resistant measure…meaning that it is
sensitive to the influence of extreme
observations.
Ex 1. Find the mean number of home
runs Hank Aaron hit in his first 21 major
league seasons.
13
27
26
44
30
39
40
34
45
44
24
32
44
39
29
44
38
47
34
40
20
Measuring Center
 Median:
◦ The midpoint of the distribution with the
observations arranged in numerical order
from least to greatest.
◦ Resistant Measure…meaning extreme
observations do not affect the median.
Ex 2. Find the median number of home
runs Barry Bonds hit in his first 16
seasons.
16
19
24
25
25
33
33
34
37
37
40
42
46
49
73
34
Comparing Mean and Median

Determines the shape of a distribution.
◦ Symmetric Distributions:
 The mean and the median are exactly the same.
◦ Left Skewed Distributions:
 The mean is to the left of the median.
◦ Right Skewed Distributions:
 The mean is to the right of the median.
Measuring Spread

Range:
◦ The difference between the largest and smallest
observations.
◦ Determines the full spread of the data.

Interquartile Range:
◦ Improves the description of the spread by looking
at the middle half of the data.
◦ IQR = Q3 – Q1
◦ Observations that fall outside this range help
identify outliers.
Quartiles
1.
Quartile 2:
1. Represents 50% of the observations.
2. The median.
2.
Quartile 1:
1. Represents 25% of the observations.
2. Find a second median of the left side of the
observations not including the 2nd quartile.
3.
Quartile 3:
1. Represents 75% of the observations.
2. Find a third median of the right side of the
observations not including the 2nd quartile.