Histograms
Name ___________________________________
Date ____________________________________
Homeroom_____________________________
DAY 65
Do Now
1. Seven teachers were asked how many miles they lived from work. The responses were 15, 7, 14, 21, 5, 9 and
13. Find the following:
a) Median
c) Mean/average
b) Mode
2. A sample of eight students were randomly selected and asked, "How many times did
you check your email yesterday?" The numbers were: 3, 0, 8, 7, 10, 2, 6, 12. What is the average?
Bonus: a ninth student was asked the same question. After adding his number to the data set, the average went
up to 7. How many times did he check his email?
Objective: SWBAT describe the overall shape of data represented in a ___________________.
Jot & Talk: Why do we use graphs to display data? Why don’t we simply put all of our information in
tables and equations?
Histograms: Grown Up Dot Plots
Know/Observed
Want to know
Learned
1.
1.
1.
2.
2.
2.
3.
3.
3.
Histograms vs. Dot Plots
The histogram to the left and dot plot to the right both
display the exact same data about cherry trees. How are
the graphs different?
Interpreting histograms
 Histograms show the __________________ of data over
equal _________________.
 The y-axis always shows _______________________.
A Toyota Highlander gets 15 miles per gallon.
Which bar should it
be in?
 Each interval ____________ the smaller number but ______________________ the largest number
o For example: the bar between 5 and 10 includes the numbers ________________________.
a) According to the histogram, there are ____ SUV’s that get between 10 and 15 miles per gallon
b) True/False: It is possible that the Honda CR-V gets 12 mpg, the Toyota RAV4 gets 13 mpg, and
the Jeep Grand Cherokee gets 13 mpg. If false, explain why not.
c) True/False: It’s possible that the Ford Escape, Mazda CX-5, and Subaru Forester all get 10 mpg.
Check for understanding: powerpoint
Group Practice
The 3 histograms below show the batting averages of the winners of the batting title in the major league
baseball (for both the American & National leagues) for certain years in the 1900s. Batting average shows the
percent (written as a decimal) of the time a certain player gets a hit. A player who has a batting average of
0.405 has gotten a hit in 40.5 % of the times that they were at bat. The batting title is an award given to the
player with the highest batting average for a given season. Refer to the histograms as you answer questions 1
– 6.
Batting Title Averages 1901 - 1930
Batting Title Averages 1931 - 1960
14
Number of Players
Number of Players
12
10
8
6
4
2
0
00
0.3
.300
12
10
8
6
4
2
0
.350
50
0.3
00
0.4
00
0.3
.400
Batting Average
.300
.350
50
0.3
Batting Average
00
0.4
.400
Batting Title Averages 1961 - 1990
Number of Players
20
15
10
5
0
00
0.3
.300
.350
50
0.3
Batting Average
00
0.4
.400
_________
1.
How many batting titles were won with a batting average of between 0.300 –
0.350 from 1901 to 1930?
_________
2.
How many batting titles were won with a batting average of between 0.300 –
0.350 from 1931 to 1960?
_________
3.
How many batting titles were won with a batting average of between 0.300 –
0.350 from 1961 to 1990?
4.
If you were to find the mean of each of the winning batting averages for each time period, which
time period do you think would have the highest mean? Explain.
__________________________________________________________________________
__________________________________________________________________________
5.
As the century progressed, what in general happened to the batting averages of the batting title
winners? Explain.
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
For questions 6 – 10, refer to the following 2 histograms. These histograms were made in an attempt to
determine if William Shakespeare was really just a pen name for Sir Francis Bacon. (A pen name is a fake
name used by another person when writing). A few scholars have had this idea and in order to determine if
this was true, a researcher had to count the letters in every word of Shakespeare’s plays & Bacon’s writing
(and you thought you had a lot of homework). Their results are recorded in the histograms below.
30
25
20
15
10
5
0
1
2
3
4
5
6
7
Letters per Word
_________
_________
_________
_________
Words Used in Bacon's Writings
Percent of Total Words
Used
Percent of Total Words
Used
Words Used in Shakespeare's Plays
6.
7.
8.
9.
8
9 10+
25
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10+
Letters per Word
What percent of all Shakespeare’s words are 4 letters long?
What percent of all Bacon’s words are 4 letters long?
What percent of all Shakespeare’s words are more than 5 letters long?
What percent of all Bacon’s words are more than 5 letters long?
10.
Based on these histograms, do you think that William Shakespeare was really just a pen name for Sir
Francis Bacon? Explain.
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
Hours of Sleep Per Night for Urbandale
Students
Percent of Students
Percent of Students
Hours of Sleep Per Night for
Wheatland Students
50
40
30
20
10
0
0
2
4
6
8
10
12
Hours of Sleep per Night
14
50
40
30
20
10
0
0
2
4
6
8
10
12
14
Hours of Sleep per Night
Suppose that the two histograms above show the sleeping habits of the teens at two different high schools.
Wheatland High School is a small rural school consisting of 100 students while Urbandale High School is
located in a large city and has 3,500 students.
_________
11.
About what percent of the students at Wheatland get at least 8 hours of sleep
per night?
_________
12.
About what percent of the students at Urbandale get at least 8 hours of sleep
per night?
_________
13.
Which high school has more actual students that sleep between 9 – 10 hours
per night?
_________
14.
Which high school has a higher median sleep time?
Histogram Mini Quiz 65
Name__________________
1. What percent of Wheatland Students got between 8 and 9 hours of sleep per night?
a. 45
b. 10
c. 30
d. 40
2. What percent of Urbandale Students got between 8 and 9 hours of sleep per night?
a. 10
b. 29
c. 18
d. 22
3. Is it possible that no one at Wheatland sleeps for exactly 7 hours each night? Justify your answer in a
complete sentence.
Histogram Mini Quiz 65
Name__________________
1. What percent of Wheatland Students got between 8 and 9 hours of sleep per night?
a. 45
b. 10
c. 30
d. 40
2. What percent of Urbandale Students got between 8 and 9 hours of sleep per night?
a. 10
b. 29
c. 18
d. 22
3. Is it possible that no one at Wheatland sleeps for exactly 7 hours each night? Justify your answer in a
complete sentence.
Skew in Histograms
Name___________________
1. Describe the skew of the histograms based on your definitions.
2. What is the difference between a histogram and a bar graph? How are they alike and how are they
difference? Write at least 2 complete sentences.
3. How would you estimate the total number of students who were
included in the survey for your data set? Explain your reasoning.
4. Could you list the exact heights of the 10 trees between 75 and
80 feet? Why or why not?
5. a) There is a gap between $2.50 and $3.00.
What does that tell you about possible prices for
cards?
b) Could you create a dot plot from the histogram? Why or why not? Write your answer in a complete
sentence.
Histograms
Name ___________________________________
Date ____________________________________
Homeroom_____________________________
65
Homework
1)
The histogram at right shows the
frequency distribution of the ages
of winners of the Nobel Prize in
Medicine at the time of winning.
Francis Crick was 46 and James
Watson was 34 when they were
jointly awarded a Nobel Prize in
Medicine in 1962.
Nobel Prize Winners by Age
60
Number of Winners
50
a) According to the histogram,
most winners are between what
age when they are awarded a
Nobel Prize?
40
30
20
10
0
30-39
40-49
50-59
60-69
70-79
80-89
Age at time of winning
b) How many scientists have been
between the ages of 80-89 at the time of winning a Nobel Prize in Medicine?
c) How would you describe the distribution of the histogram?
2) The histogram below categorizes data collected based on the number of genes seen in a species.
Number of Genes in Select Species
Number of Species
3.5
3
2.5
2
1.5
1
0.5
0
< 1,000
1,0015,000
5,00110,000
10,00115,000
Number of Genes
a) How many species had between 10,001 and 15,000 genes?
b) How many total species were involved in this study?
15,00120,000
>20,000
c) How many species showed less than 20,000 total genes?
d) Is the histogram symmetric? Why or why not?
d) Is the data in graph 2 sufficient to reveal a trend in the number of genes per species?
Explain your reasoning.