# File

```Warm Up!
• Write down objective and homework in
agenda
• Lay out homework (none!!)
• Homework (Box Plot wkst)
• Get Graph Paper!
Unit 2 Common Core Standards
•
•
•
•
•
•
•
•
•
•
•
•
MP.1 Make sense of problems and persevere in solving them.
MP.2 Reason abstractly and quantitatively.
MP.3 Construct viable arguments and critique the reasoning of others.
MP.4 Model with mathematics.
MP.5 Use appropriate tools strategically.
MP.6 Attend to precision.
N-Q.1 Use units as a way to understand problems and to guide the solution of
multi-step problems; choose and interpret units consistently in formulas; choose
and interpret the scale and the origin in graphs and data displays.
N-Q.2 Define appropriate quantities for the purpose of descriptive modeling.
N-Q.3 Choose a level of accuracy appropriate to limitations on measurement when
reporting quantities.
S-ID.1 Represent data with plots on the real number line (dot plots, histograms, and
box plots).
S-ID.2 Use statistics appropriate to the shape of the data distribution to compare
center (median, mean) and spread (interquartile range, standard deviation) of two
or more different data sets.
S-ID.3 Interpret differences in shape, center, and spread in the context of the data
sets, accounting for possible effects of extreme data points (outliers).
Warm Up
• Residents of upstate New York are accustomed to
large amounts of snow with snowfalls often
exceeding 6 inches in one day. In one city, such
snowfalls were recorded for two seasons and are
as follows (in inches):
8.6, 9.5, 14.1, 11.5, 7.0, 8.4, 9.0
What are the mean and the standard deviation
for this data, to the nearest hundredth?
• Work by hand, but you may check your work with
a calculator! 
Answsers
• Mean: 9.7 inches
• Standard Deviation: 2.18
Vocabulary
• Box Plot: a graphic representation of a
distribution by a rectangle, the ends of which
mark the maximum and minimum values, and
in which the median and first and third
quartiles are marked by lines parallel to the
ends.
Describing Data Graphically
Quantitative Data
• Dotplot
• Histogram
• Boxplot
S-ID.1 Represent data
with plots on the real
number line (dot plots,
histograms, and box
plots).
Describing Data Numerically – Unit 2
• Measures of Center –
mean, median
range, interquartile
range, standard
deviation
S-ID.2 Use statistics appropriate to
the shape of the data distribution
to compare center (median, mean)
standard deviation) of two or more
different data sets.
Boxplots
Min
Q1
Median
Q3
Lower
Upper
Quartile
Quartile
Max
Distribution Example: The shape of our distribution is skewed right since the right whisker is a
lot longer than the left whisker. The center is the line in the middle of the box that corresponds
to the median. For the spread we can easily see how far out each whisker reaches (the range).
We can also look at the IQR.
• Range: max – min; spread of the entire data
set – sensitive to outliers
• IQR: Q3 – Q1; spread of the middle 50% of the
data – not sensitive to outliers
2
• Standard Deviation:
(
x


)


n
the typical amount that a data value will vary
from the mean – sensitive to outliers
How do you decide whether
to use the mean and
standard deviation or the
median and IQR to
summarize the data
numerically?
Outliers
• In general, the mean and standard deviation
are more sensitive because their formulas take
every data value into account
• The median and IQR do not, they only look at
the “middle” of the data and therefore are not
influenced by the presence of outliers
• For describing skewed distributions the fivenumber summary, instead of the Mean and
Standard Deviation, is preferred.
• For describing symmetric distributions the
mean and standard deviation are preferred.
46
50
Boxplots
61
70
56
Min
Q1
Median
Q3
Lower
Upper
Quartile
Quartile
Max
Describe the Distribution if the box plox data is “Money
spent at Target”
Box Plot by hand
• Order the numbers from least to greatest
• Find the 5 number summary
– Min, 1st quartile, median, 3rd quartile, Max
• Draw a Number line
Box Plot
• The heights, in feet, of suspended roller
coasters in the United States are given below.
• 35 42 42.5 60 60 70 76 78 81 100
• Create a Box Plot from the data, then describe
the distribution
Box Plots
• The number of DVDs rented each day over
two weeks at a video rental store are given.
Make a box-and-whisker plot of the data.
• 38 42 50 65 82 91 88 40 34 41 71 93 87 94
• Describe the distribution of the box plot
You Try!
• Ages of roller rink employees: 24, 22, 30, 18,
29, 38, 33, 17, 22, 25, 16, 41
• Create a box plot and describe it’s distrubtion
You Try!
• Given the following grades on an English test:
• 91, 98, 87, 76, 100, 45, 72, 85, 92, 88, 87, 90,
91, 66, 100, 99, 67, 85, 79, 80, 85
• Describe the distribution of this graph
Practice!
Below is a stem and leaf plot of the amount of
money spent by 25 shoppers at a grocery store.
Stem
Leaf
0
1
2
3
4
5
6
7
8
9
10
11
3
0
0
1
2
0
5
2
7
3
6
1
0
3
5
7 8 9
3 6 8
4 7
5
6
Key: 42 = \$42
Practice!
Stem
Leaf
0
1
2
3
4
5
6
7
8
9
10
11
3
0
0
1
2
0
5
2
6
1
0
3
5
7 8 9
3 6 8
4 7
5
6
7
3
Key: 42 = \$42
a) Calculate the mean and
median.
b) Calculate the lower and upper
quartiles and IQR. (make a box
plot on the calculator!)
c) Determine which, if any, values
are outliers.
d) Write several sentences to
describe this data set in
context.
e) Name some factors that might
account for the extreme
values, and the much lower
measure of center.
Test Prep
• In the table below, the public high school graduation rates for
1992-1993 are given for each state, including the District of
Columbia. (Note: the rates are listed in ascending order)
Test Prep
1. Find the mean
2. Find the median
3. Which measure of center would be the most
with a reason.
4. Calculate the 5 number summary Find the
range.
5. Find the interquartile range. Interpret what
this gives you.
Test Prep
6. List the 7 states that have the highest graduation rates.
What region of the country to they represent?
7. List the 7 states that have the lowest graduation rates.
What region of the country do they represent?
“6” and “7.”
9. Are there any outliers?
10. What graduation rate would a state have to be over or
under to be considered an outlier?
11. Create an outlier. Identify it here and explain (good or bad
12. Add this outlier to the data. Recalculate the mean and
median.
13. As a North Carolinian, what does this outlier do for the