Pictures of data
• Dot plot or line plot
• Histogram
• Box and Whiskers plot
Dot plot for the sugar in cereal
Common Shapes of a distribution
height of students in a class
income distribution
test scores from an easy test
The 5 number summary and the box and
whisker plot.
• A distribution can be broken up
into quarters. To do this you
need a 5 number summary
• Minimum q1 Median, q3,
Maximum
• To find the median simply
determine the number of data
points n, then add 1 and divide
𝑛+1
by 2
2
• Then count up from the
beginning.
• 3,4,6,8,9,11,12,14,
8+1
2
= 4.5
• Halfway between 8 and 9 or 8.5
Analyzing a box plot
Box plot for sugar in breakfast cereals
• Data distribution
• 1,3,4,4,4,5,5,6,7,7,7,7,8,10,10,11,11,12,13,22
Minimum
Q1
Median
Q3
Maximum
Box plot video
• http://www.learner.org/vod/vod
_window.html?pid=3139
Making a histogram
Number of times you visited a
store during Christmas break
0,0,1,1,2,2,2,3,3,4,5,6,8,8,9,10
• Determine intervals
•0≤𝑥<2
• 2≤ 𝑥 <4
•4≤𝑥<6
• 6≤ 𝑥 < 8
• 8 ≤ 𝑥 < 10
Analzying a histogram
• Shape
• Outliers
• Center
• Spread
Analysis
• Shape
• Outliers
• Center
• Spread
Histogram video
• http://www.learner.org/vod/vod
_window.html?pid=3137
Analysis
• Shape
• Outliers
• Center
• Spread
Analysis
• Shape
• Outliers
• Center
• Spread
4 things to look for in a distribution
• Shape symmetric, left skew,
right skew
• Outliers; data that lies outside
the range of most of the data
• Center; median, mean
• Spread; IQR, Standard deviation,
range How much the data is
spread out.
8.2 Measures of center
Mean
• Find the mean for the amount of
sugar in the box of a cereal from
the 8.1 data set given below.
• 1,,3,4,4,4,5,5,6,7,7,7,7,8,10,10,1
1,11,12,13,22
• Compare the mean to the
median.
• Explain the difference between
the mean and the median.
Compare the two measures of center. Page
475
Analysis mean or median
Analysis mean or median
Analysis mean or median
• What will determine if you use
the mean or the median to
represent the center of a data
distribution?
• What kind of shape does a
distribution have if the mean
and the median are the same.
• What kind of shape does a
distribution have if the mean is
bigger than the median?
• What kind of shape does a
distribution have if the mean is
smaller than the median?
Analysis practice
What kind of distribution?
Symmetric, left skewed, right skewed
• Mean
102
• Median 103
What kind of distribution?
Symmetric, left skewed, right skewed
• Mean 77
• Median 52
What kind of distribution?
Symmetric, left skewed, right skewed
• Mean 48
• Median 61
Outliers by Malcome Gladwell
• The main tenet of Outliers is that there is a logic behind why some people become
successful, and it has more to do with legacy and opportunity than high IQ. In his latest
book, New Yorker contributor Gladwell casts his inquisitive eye on those who have risen
meteorically to the top of their fields, analyzing developmental patterns and searching
for a common thread. The author asserts that there is no such thing as a self-made man,
that "the true origins of high achievement" lie instead in the circumstances and
influences of one's upbringing, combined with excellent timing. The Beatles had
Hamburg in 1960-62; Bill Gates had access to an ASR-33 Teletype in 1968. Both put in
thousands of hours-Gladwell posits that 10,000 is the magic number-on their craft at a
young age, resulting in an above-average head start.
Gladwell makes sure to note that to begin with, these individuals possessed once-in-ageneration talent in their fields. He simply makes the point that both encountered the
kind of "right place at the right time" opportunity that allowed them to capitalize on
their talent, a delineation that often separates moderate from extraordinary success.
This is also why Asians excel at mathematics-their culture demands it. If other countries
schooled their children as rigorously, the author argues, scores would even out.
8.3 IQR and outliers
Does the distribution have any outliers
outliers? Explain.
Answer questions 1-5 with the following box
plots.
8.4 Standard deviation
• Joe score’s the following points
in each of 5 basketball games
• 6,8,10,12,14
• Sally score’s the following points
in each of 5 basketball games.
• 2,6,10,14,18
• Determine the mean, median
and range.
• Standard deviation is the
average distance from the mean.
• Since it is measuring the
distance from the mean and the
mean only works for symmetric
distributions, the standard
deviation should only be used
for symmetric distributions.
Average distance
from mean data
value - mean
6-10 = -4
16
8 -10 = -2
4
10-10 = 0
0
12 -10 = 2
4
14-10 = 4
16