warmup what is the graph telling you?. lesson 9 data display
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Warmup
What is the graph telling you?
Lesson 9 Data Display
Words vs. Data Display
The students in Mr. Math’s geometry class scored 75, 80, 90, 85, 75, 95, 95, 75, 85, 90, 95, 85, 85, 85, 75, 80, 85, 95, 90, 85, 75, 80, 75, 80, and 85 on a recent exam.
Grade Frequency
75 6
80 4
85 8
90 3
95 4
Words vs. Table
Jennifer ran 5 minutes on the treadmill each day for her first week. During each additional week, she added 1 minute to her daily time. Make a table of her daily time for each of the first five weeks of using the treadmill.
Week Daily Time
Words vs. Matrix
Juan saw 6 horror, 3 drama, and 2 documentary movies in the past month. Matt viewed 7 drama, 4 documentary, and 3 horror movies during the same time. Make a matrix to show their movie viewing.
Words vs. Frequency Chart
Make a frequency chart of the ages of students in this class.
Age Tally Frequency
Words vs. Stem-and-Leaf
Organize the collection of data into a stem-and-leaf plot.
15 30 17 16 27 22 31 5 16 8 24
Khan Academy Stem-and-Leaf Video Lesson
Stem and Leaf Interactive
Another Type of Stem-and-Leaf Plot
The back-to-back stem-and-leaf plot shows the ages of members of the U.S men’s and women’s 2004 Olympic gymnastics teams. Compare the ages of the gymnasts on the two teams.
Gymnastics
Words vs. Box-and-Whiskers
Box-and-WhiskersFind the median (half-way point when data is in order) then find the lower quartile (median of the bottom half) and upper quartile (median of the top half). Label the line with the minimum being near the left and the maximum being near the right of the line.
Khan Video on Box-and-Whiskers
Words vs. Box-and-Whiskers
Make a box-and-whiskers of the following recent test scores.
71, 85, 73, 95, 98, 77, 71, 86, 100, 82, 89
Make your own box-and-whiskers on-line.
EXAMPLE 2 Interpret a box-and-whisker plot
Precipitation
The box-and-whisker plots below show the normal precipitation (in inches) each month in Dallas and in Houston, Texas.
a. For how many months is Houston’s precipitation less than 3.5 inches?
EXAMPLE 2 Interpret a box-and-whisker plot
SOLUTION
a. For Houston, the lower quartile is 3.5. A whisker represents 25% of the data, so for 25% of 12 months, or 3 months, Houston has less than 3.5 inches of precipitation.
Words vs. Line Plot
Organize the following test scores into a line plot.
70 75 80 75 70 100 95 75 70 85 80 75 75 70 85 90 95 95 85 70 75 85 90 75 90 85 85 75 70 90 95 90
What is an outlier?
A outlier is data that is numerically distant from the other data.
Example: The teacher’s age alongside the ages of the students in this class.
EXAMPLE 2 Interpret a stem-and-leaf plot
SOLUTION
Consider the distribution of the data. The interval for 10–19 years old contains more than half of the female gymnasts. The interval for 20–29 years old contains more than half of the male gymnasts. The clustering of the data shows that the men’s team was generally older than the women’s team.
GUIDED PRACTICE
Television
The back-to-back stem-and-leaf plot shows the percents of students in 24 countries who report watching television for 4 or more hours each day. Compare the data for female and male students.
GUIDED PRACTICEPrecipitation
In Example 2, for how many months was the precipitation in Dallas more than 2.6 inches?
SOLUTION
For Dallas, the greater quartile is 2.6, A whisker represent 50% of the data, so for 50% of 12 months, or 6 months, Dallas has more than 2.6 inches of precipitation.
Temphumidity
80 84 88 92 96 100 104 108
40 80 83 88 94 101 109 119 130
50 81 85 95 103 113 118 131
60 82 88 95 105 116 129
70 83 90 100 112 126
80 84 94 106 121
90 86 98 113 131
100 87 103 121
Heat Index
The table above represents how the air temperature combines with the humidity to form the heat index. Tell if each of the following statements is true or false.
1. As the humidity and temperature decrease, the heat index increases.2. As humidity decreases and the temperature increases, the heat index decreases.3. As the humidity and temperature increase, the heat index increases.4. As the humidity and temperature increase, the heat index decreases.5. As humidity increases and the temperature decreases, the heat index increases.6. As the humidity and temperature decrease, the heat index decreases. 7. As humidity increases and the temperature decreases, the heat index decreases.8. As humidity decreases and the temperature increases, the heat index increases.
Heat IndexANSWERS
Temphumidity
80 84 88 92 96 100 104 108
40 80 83 88 94 101 109 119 130
50 81 85 95 103 113 118 131
60 82 88 95 105 116 129
70 83 90 100 112 126
80 84 94 106 121
90 86 98 113 131
100 87 103 121
The table above represents how the air temperature combines with the humidity to form the heat index. Tell if each of the following statements is true or false.
1. As the humidity and temperature decrease, the heat index increases. False2. As humidity decreases and the temperature increases, the heat index decreases.
False3. As the humidity and temperature increase, the heat index increases. True4. As the humidity and temperature increase, the heat index decreases. False5. As humidity increases and the temperature decreases, the heat index increases.
False6. As the humidity and temperature decrease, the heat index decreases. True7. As humidity increases and the temperature decreases, the heat index decreases.
True8. As humidity decreases and the temperature increases, the heat index increases.
True
50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98
Note: On a box-and-whiskers graph, each part of the graph represents 25% of the scores.
1. What was the minimum score?2. What was the maximum score?3. What is the median score?4. What is the lower quartile score?5. What is the upper quartile score?6. What percentage of the scores is greater than 74?7. What percentage of the scores is less than 82?8. What percentage of the scores is between 74 and 91?
BOX-AND-WHISKERS Graph
ANSWERS
50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98
BOX-AND-WHISKERS GraphNote: On a box-and-whiskers graph, each part of the graph represents
25% of the scores.1. What was the minimum score?2. What was the maximum score?3. What is the median score?4. What is the lower quartile score?5. What is the upper quartile score?6. What percentage of the scores is greater than 74?7. What percentage of the scores is less than 82?8. What percentage of the scores is between 74 and 91?
1. Which country has had the highest unemployment rate? 2. When did the minimum unemployment rate occur?3. Estimate the unemployment rate for Europe in 2001.4. During what year did the United States experience the lowest unemployment rate?5. If the trend continued, what was the likely unemployment rate for Japan in 2007?
ANSWERS
1. Which country has had the highest unemployment rate? Canada 2. When did the minimum unemployment rate occur? 19913. Estimate the unemployment rate for Europe in 2001. 7.8%4. During what year did the United States experience the lowest unemployment rate? 20005. If the trend continued, what was the likely unemployment rate for Japan in 2007? 3.8%
1. Which activity is most popular?2. Which activity(ies) are the least
popular?3. Which activities have the mode
popularity?4. Which activities have > 10% rate
of engagement?5. Which activities have < 1% rate
of engagement?6. Which activities have
1.2 < engagement % < 2.07. Which is more popular… a. golfing or running? b. hiking or cycling? c. basketball or weightlifting? d. dancing or rollerblading?
ANSWERS1. Which activity is most popular? walking2. Which activity(ies) are the least popular?
Hockey, wrestling, gymnastics3. Which activities have the mode popularity?
Mode means most frequent occurences…equestrian, rollerblading, skiing…hockey, wrestling, gymnastics
4. Which activities have > 10% rate of engagement? Walking, weightlifting, cardio
5. Which activities have < 1% rate of engagement? Volleyball, hiking, martial arts, equestrian, rollerblading, skiing, hockey, wrestling, gymnastics
6. Which activities have 1.2 < engagement % < 2.0 cannot be = to 1.2 but can be equal to 2.0 and everything in between…bowling, racquet sports, football, softball, dancing, yoga
7. Which is more popular… a. golfing or running? running b. hiking or cycling? cycling c. basketball or weightlifting? weightlifting d. dancing or rollerblading? dancing
110
100
90
80
70
60
50
Month
Tem
pera
ture
(°F
)
Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec
Average Daily Temperature
1. Which month has the maximum average daily temperature?
2. Which month has the minimum average daily temperature?
3. What is the range of temperatures?
4. What is the likely mean temperature for the month of June?
5. Does the graph represent the chart to the right? (yes or no)
Month Mean Temperature
Jan 60
Feb 70
Mar 78
Apr 82
May 90
June
July 108
Aug 102
Sept 98
Oct 95
Nov 98
Dec 100
ANSWERS110
100
90
80
70
60
50
Month
Tem
pera
ture
(°F
)
Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec
Average Daily Temperature
1. Which month has the maximum average daily temperature? July2. Which month has the minimum average daily temperature? January3. What is the range of temperatures? Maximum – Minumum = 108 – 60 =
484. What is the likely mean temperature for the month of June? Around 1005. Does the graph represent the chart to the right? (yes or no) No
Month Mean Temperature
Jan 60
Feb 70
Mar 78
Apr 82
May 90
June
July 108
Aug 102
Sept 98
Oct 95
Nov 98
Dec 100
Using the tax table, specify the tax for the following.
• single with taxable income of $32,175• head of household with taxable income of
$32,725• married, filing jointly, with taxable income
of $32,503• married, filing separately, with taxable
income of $32,698• single with taxable income of $32,550• head of household with taxable income of
$32,400
ANSWERSUsing the tax table, specify
the tax for the following.
• single with taxable income of $32,175 • head of household with taxable income of
$32,725• married, filing jointly, with taxable income
of $32,503• married, filing separately, with taxable
income of $32,698• single with taxable income of $32,550• head of household with taxable income of
$32,400
Assignment
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