Download Group - Wando High School

Name __________________________Statistics: Histograms, Stem and Leaf Plots, and Dot Plots
These four graphs all display the same data--the Kentucky Derby winning times. The dot plot is a
horizontal version of the graph shown in your book.
1. Describe fully in context what each lettered part represents about the data.
A
B
A
C
D
E
B
E
C
17 : 2
D
16 : 5
16 : 000113
15 : 5777777888899
15 :
14 :
14 :
13 : 5
13 : 00111233
12 : 555555555555556667777888888999999
12 : 0001111111111222222222222222222222222222223333333333333334444444444444
11 : 9
(13:5 means a winning time of 135 seconds)
2. What are the similarities and differences of each graph?
3. When might you choose to display data using a stem and leaf plot instead of a histogram?
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Name _____________________________________________
Statistics: Frequency Tables
1. Here is a frequency table showing how nuclear power plants are
distributed across the United States.
a. Explain what the pair (2, 11) in this table represents in the context
of the problem.
______________________________________________________
______________________________________________________
# plants
0
1
2
3
4
5
6
# states
19
12
11
4
2
1
1
b. Find the mean and median and describe these values in context.
Mean:
Median:
2. Here is a frequency table of the ages of U.S. Presidents when
they were first inaugurated into the office.
a. Which interval contains the median age of inauguration?
b. Estimate the mean age of inauguration of U.S. Presidents
(use the center of each interval)
Age at
inauguration
40-44
45-49
50-54
55-59
60-64
65-69
Number of
Presidents
2
7
13
12
7
3
3. Estimate the mean and median of the data
shown in this histogram.
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Name ______________________________________
Statistics: The 5 Number Summary
1. Pediatricians use percentiles to monitor the height and weight of their patients over time.
According to the Centers for Disease Control, the distribution of weights of 5 year old males
has the following quartiles:
1st quartile: 37 pounds
2nd quartile: 40 pounds
3rd quartile: 42 pounds
a. For each quartile, write a sentence that describes what that quartile means about the
weights of 5 year old males.
Q1:
Q2:
Q3:
b. What percent of 5 year old males weigh…
between 37 and 40 pounds
less than 40 pounds
more than 40 pounds
more than 37 pounds
between 40 and 42 pounds
less than 37 pounds
c. Mark is a 5 year old of average height who weighs 38 pounds. Is his weight also average?
Explain your thinking.
2. Here again is the dot plot of the 135 Kentucky Derby winning times. Use the dot plot to
separate the dots into quartiles, then draw a box and whisker plot above the dots on the same
axis. On the back, describe the shape, center, and spread of the distribution of winning times
in context.
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Name ______________________________________
Statistics: Standard Deviation
A class has been divided into groups of five students each. The groups have completed an
independent study project, and at the end they take an individual 20-point quiz. Here are the
scores, by group:
Group
Quiz
Scores
(out of 20)
1
10
10
10
10
10
2
8
10
10
10
12
3
0
10
10
10
20
4
0
8
10
12
20
5
0
2
10
18
20
6
4
6
8
14
18
Mean
Median
Range
1. Find the mean and median for each group. How well do these measures of center alone
describe the differences among these groups?
2. Find the range for each group. How well does this measure of spread reflect the differences in
these distributions?
3. Calculate the standard deviation for each group. Use the table below to organize your
calculations. (D = Deviation of that quiz score from the mean for that group)
Group 1
D D2
10
10
10
10
10
Score
Group 2
D D2
8
10
10
10
12
Score
Group 3
D D2
0
10
10
10
20
Score
Group 4
D D2
0
8
10
12
20
Score
Group 5
D D2
0
2
10
18
20
Score
Group 6
D D2
4
6
8
14
18
Score
Sum of
D2
Divide
by n-1
Square
root
(SD)
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Score
4. Make a dot plot of each group’s scores on the scale below. The first two groups are done for
you.
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
Ɣ
ƔƔƔƔƔ
ƔƔƔ
Ɣ
1
2
3
4
5
6
Group
5. Examine the dotplot. How does the standard deviation of each group describe the spread of
each group compared to the spread of the other groups?
Group 1:
Group 2:
Group 3:
Group 4:
Group 5:
Group 6:
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Name ______________________________________
Statistics: More with Histograms
1. Sketch histograms that meet the following descriptions. Also, describe the shape of each
distribution.
a) The mean, median, and the mode are almost
equal.
b) The mean is less than the mean.
c) The mean, median and mode are all
different from each other.
d) The mean and median are almost equal but
the mode is different.
2. For each example above, tell whether is is best to describe the data using the mean and the
standard deviation or the median and the IQR.
3. Decide whether each set of data below could be displayed in either a bar graph or a histogram.
On the back, draw and label that graph, and justify your choice.
Set A
Set B
Height
(inches)
Number of
children
40-44
45-49
50-54
55-59
60-64
4
7
3
1
1
Set C
Color
frequency
of hair
Brown
Blonde
Red
Black
Shoe
size
shoes in
stock
5
6
7
8
9
44
26
74
62
48
112
234
45
77
Set D
Number of
commercials during
selected TV movies
15, 14, 16, 10, 16, 16,
13, 14, 15, 12, 10, 11,
19, 13, 15
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