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