Transcript Standard Deviation - about NumberBender

Standard
Deviation
Warm-up
Do girls study more than boys? We
asked the students in three AP Statistics
classes how many minutes they studied
on a typical weeknight. Here are the
responses of random samples of 30 girls
and 30 boys from the classes:
WARM-UP
1. Construct a back-to-back
boxplot for this data.
2. Compute for the
numerical summary of this
data.
3. Find the outliers for both
male and female
respondents.
4. Describe the distribution
of each data set by looking
at your boxplots. What will
be your conclusion about
the male/female study
habits base on your
statistical data.
Standard Deviation
The standard deviation measures
spread by looking at how far the
observations are from their mean
Example
A population consists of four observations: {1, 3, 5, 7}.
What is the variance? What is the standard deviation?
x
= 1+3+5+7 = 4
4
s2 =(1-4)2 + (3-4)2 +(5-4)2 +(7-4)2
s= √ 6.67
(4-1)
s2
=(-3) 2 +
(-1) 2
+(1) 2
+(3) 2
(3)
s2
9+1+1+9
3
=
20
3
= 6.67
s= 2.58
Properties of Standard
Deviation
s measures spread about the mean and should be
used only when the mean is chosen as the measure of
center.
•
s = 0 only when there is no spread/variability. This
happens only when all observations have the same
value. Otherwise, s > 0. As the observations become
more spread out about their mean, s gets larger.
•
s, like the mean x, is NOT resistant. A few outliers
can make s very large.
Choosing Measures of Center
and Spread
5-number summary VS x and s
The 5-number summary is usually better
than the mean and standard deviation
for describing a skewed distribution with
strong outliers.
5-number summary
x and s
NTERPRETING NUMERICAL DATA
S
The distribution of the C-section performed by the MALE
doctors is more skewed to the right while for the female
doctors has approximately symmetrical distribution
O
Two male physicians performed an unusually high number
of cesarean sections, 85 and 86. I used the 1.5xIQR rule
to verify these outliers
C
The mean and median numbers of cesarean sections performed are
higher for the male doctors. More than half of the female doctors in
the study performed fewer than 20 cesarean sections in a year.
S
Both the standard deviation and the IQR for the male
doctors are much larger than the corresponding statistics for
the female doctors. So there is much greater variability in
the number of cesarean sections performed by male
Statistical tools
Describing SOCS and skewness
Constructing dotplots and stemplots
Describing the SOCS of your distribution
Creating histogram
Generating histogram using graphing calculator
Organizing data by FDT
Constructing ogive and finding percentile using ogive.