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AP Statistics
HW: p.48-52 #39, 43,44, 45
Lab due next class
Obj: to use variance and standard deviation
Do Now:
1. Make a modified box plot for the # of home runs hit by
Babe Ruth in each of his seasons as a Yankee:
54, 59, 35, 41, 46, 25, 47, 60, 54, 46, 49, 46, 41, 34, 22
2.
Give the “five-number summary” for this data set.
3.
Type the data into L1 and use the calculator to make a
modified box plot.
C 1, D 8
Standard Deviation
• Give a numerical value to the spread of a
distribution
– If you give mean as the center, give standard
deviation as the spread.
– If you give the median as the center, give
range as the spread.
• To calculate std. dev. you must first
calculate variance.
Variance
• Notation: s2
• For a data set with mean = x
observations: x1, x2, …, xn
and n
2
2
2
(
x

x
)

(
x

x
)

...

(
x

x
)
2
2
n
s  1
n 1
1
2
s 
( xi  x )

n 1
2
Standard Deviation (s)
s=
1
2
(
x

x
)
 i
n 1
– Measures the spread about the mean, so
should only be used when the mean is given
as the measure of center.
– (Handout of formulas)
SOCS
• For a strongly skewed distribution, the five-number
summary is better to describe center and spread.
• Mean and standard deviation are better for symmetric
distributions. (Why?)
• For strongly skewed distributions, very high or very low
values can greatly affect the mean and standard
deviation.
*** Always plot your data first!!! ***
Try Page 52 # 40
• Compare your answers with your partner