With Ohio Graduation Test Questions

Mathematics Benchmarks & Indicators

with Ohio Graduation Test Questions

Grades 9 – 10

Includes questions from the released

2008, 2007, 2006, 2005, 2004, and 2003

Ohio Graduation Tests

Far East Regional Partnership

for Conceptually Based Mathematics

Youngstown State University

Compiled by A. Crabtree, 2006

Revised by A. Crabtree and L. Holovatick, 2007

Revised by A. Crabtree, J. Lucas, and T. Cameron, 2008

Data Analysis and Probability OGT Problems

A. Create, interpret and use graphical displays and statistical measures to describe data; e.g., box-and-whisker plots, histograms, scatterplots, measures of center and variability.

9.1. Classify data as univariate (single variable) and as bivariate (two variables) and as quantitative (measurement) or qualitative (categorical) data.

9.2. Create a scatterplot for a set of bivariate data, sketch the line of best fit, and interpret the slope of the line of best fit.

9.3. Analyze and interpret frequency distributions based on spread, symmetry, skewness, clusters and outliers.

10.2. Represent and analyze bivariate data using appropriate graphical displays (scatterplots,, parallel box-and-whisker plots, histograms with more than one set of data, tables, charts, spreadsheets) with and without technology.

10.3. Display bivariate data where at least one variable is categorical.

10.4. Identify outliers on a data display; e.g., use the interquartile range to identify outliers an a box-and-whisker plot.

10.6. Interpret the relationship between two variables using multiple graphical displays and statistical measures; e.g., scatterplots, parallel box-and-whisker plots, and measures of center and spread.

OGT 2008 – Problem # 18
The graph shows the percent of the total votes cast for each of the four candidates in Andersonville’s city council election.
If 2,542 people voted in this election, about how many votes did Lango receive? / A. 76
B. 141
C. 458
D. 915
OGT 2007 – Problem # 26
An inspector at a nail factory checks a sample of nails to measure their deviation from the standard length. Positive deviation means a nail is too long, and negative deviation means it is too short.
Based on the inspector’s chart above, what is true of the nails produced at this factory?
A. The nails produced all have the standard length.
B. The nails are much more likely to be too long than too short.
C. The nails are much more likely to be too short than too long.
D. The nails are about as likely to be too long as they are to be too short.
OGT 2007 – Problem # 43
The histogram below displays student scores on Mr. Dell’s English exam.
How many students scored below 70 on the exam? / A. 4
B. 6
C. 9
D. 13
OGT 2006 – Problem # 27
The scatterplot below indicates the number of sit-ups and push-ups completed by each student in Mr. Jenkin’s physical education class.
If Mary did 35 push-ups, approximately how many sit-ups did she complete? / A. 30
B. 35
C. 45
D. 50
OGT 2005 – Problem # 22
Ice cream vendors at the county fair gathered data about the various ages of people and their preferences for different ice cream flavors. The data are summarized in the table.
The circle graph below represents the flavor preferences for one of the four age groups.
Which age group’s preferences are represented in the graph?
A. under 12
B. 12 to 20
C. 21 to 45
D. over 45
OGT 2004 – Problem # 2
The box-and-whisker plot below describes the weights of a sample of 100 chickens.
What statement can be made about the data using the graph alone?
A. The range of the weights is 3 lb.
B. The median weight is less than 2 lb.
C. Twenty-five percent of the chickens weigh less than 1 lb.
D. Fifty percent of the chickens weigh more than 2 lb.
OGT 2004 – Problem # 34
The graph shows the population of Ohio from
1900 to 1990.
Based on the data, in which decade did the
population of Ohio increase the most? / A. 1910 to 1920
B. 1940 to 1950
C. 1950 to 1960
D. 1960 to 1970
OGT 2003 – Problem #6
Last month members of a Fostoria youth group
spent time doing community service. The graph
shows the numbers of students who contributed
certain hours of service.
How many members spent 10 or more hours in
community service last month? / A. 3
B. 4
C. 9
D. 12
OGT 2003 – Problem #16
The students at Watertown High School are raising money for homecoming. The graph shows the amount of money each class has raised so far.
About what percentage of the money raised did the sophomore class earn?
A. 25%
B. 33%
C. 43%
D. 50%
OGT 2003 – Problem #37
This box-and-whisker plot represents the
average annual precipitation in Ohio over a
ten-year period.
Which of these is the median rainfall for the
ten-year period? / A. 35.5 inches
B. 39.1 inches
C. 40.0 inches
D. 42.6 inches

B. Evaluate different graphical representations of the same data to determine which is the most appropriate representation for an identified purpose.

OGT 2008 – Problem # 39
In honor of the new millennium, Stephanie buried a time capsule in her front yard. She sketched the location of key landmarks as shown below. She noted that the capsule was buried equidistant from the oak tree and the elm tree. It is also equidistant from the mailbox and the front door.
Which pair of coordinates is the closest estimate for the location of the time capsule?
A. (4, G)
B. (7, H)
C. (8, G)
D. (10, H)
OGT 2007 – Problem # 1
Rubin used an altimeter to measure and record his height above sea level at different times during his hike in the mountains.
Which type of data display could Rubin use to show how his height above sea level changed with time? / A. line graph
B. circle graph
C. stem-and-leaf plot
D. box-and-whisker plot
OGT 2006 – Problem # 9
Which graphical representation would be most useful in comparing the change in average earnings of male employees versus average earnings of female employees over the course of a 50-year period? / A. circle graph
B. double line graph
C. box-and-whisker plot
D. back-to-back stem-and-leaf plot
OGT 2005 – Problem # 28
Susan entered a highway at 1:00. On the
highway, she had driven a total of 32 miles by
1:30, 61 miles by 2:00, and 125 miles by 3:00.
Which kind of data display would be an
appropriate way to show how Susan’s total
driving distance varied with time? / A. line graph
B. circle graph
C. stem-and-leaf plot
D. box-and-whisker plot
OGT 2004 – Problem # 29
The table shows the number of people who speak each of the six most common languages of the world.
Which type of graph is appropriate to display the data in the table?
A. bar graph
B. box-and-whisker plot
C. line graph
D. scatterplot

C. Compare the characteristics of the mean, median and mode for a given set of data, and explain which measure of center best represents the data.

10.1. Describe measures of center and the range verbally, graphically and algebraically.

OGT 2007 – Problem # 5
The noon temperatures are recorded for 7 consecutive days in Cleveland, Ohio. The sum of the 7 temperatures is positive.
Which statement about these 7 temperatures must be true?
A. The mean of the temperatures is positive.
B. The mode of the temperatures is positive.
C. The median of the temperatures is positive.
D. The minimum of the temperatures is positive.
OGT 2006 – Problem # 35
A video game company reports the sales of video games for the first 11 months.
Monthly Sales of Video Games
Month / Sales (in millions)
1 / 4.5
2 / 5.2
3 / 4.7
4 / 4.6
5 / 5.2
6 / 4.7
7 / 5.6
8 / 5.3
9 / 4.8
10 / 5.2
11 / 4.8
The company’s goal is to sell an average of 5 million games per month.
What is the minimum number of video games the company must sell in the 12th month to meet its goal? / A. 4.8
B. 5.0
C. 5.2
D. 5.4
OGT 2005 – Problem # 36
The average salary for all department store workers in a certain area is $255 a week. The weekly salaries of the 7 employees in the Acme Department Store are given in the table below.
In your Answer Document, determine the measures of center (mean, median and mode) of the 7 salaries.
Specify which of these measures of center the management could use to represent the salaries in an argument against pay increases. Explain your answer.
Specify which of these measures of center the labor union could use to represent the salaries in an argument for pay increases. Explain your answer.
OGT 2004 – Problem # 6
A set of data contains 10 negative numbers and 4 positive numbers. Which one of these statements must be true?
A. The mean is a negative number.
B. The median is a negative number.
C. The mode is a negative number.
D. The range is a negative number.

D. Find, use and interpret measures of center and spread, such as mean and quartiles, and use those measures to compare and draw conclusions about sets of data.

OGT 2008 – Problem # 15
Weekly salaries of the employees at a local video store are shown in the table below.
What is the mean weekly salary at this video store?
A. $230.48
B. $242.00
C. $322.67
D. $350.00
OGT 2007 – Problem #22
The Ohio Big Tree Program lists the largest living specimen of each kind of tree found in the state. Three measurements are needed to assign a score to each tree:
Circumference (1 inch = 1 point)
Height (1 foot = 1 point)
Average crown spread (1 foot = 1/4 point)
The score is found by adding the number of points for each measurement.
Four trees and their measurements are given below.
In your Answer Document, calculate the scores for each of the four trees in the table. Arrange the trees in order based on their scores. Show work or provide an explanation to support your answer.
Write a formula for computing the score assigned by the Ohio Big Tree Program.
OGT 2007 – Problem # 31
A construction company buys $38,400 worth of new equipment, the value of which decreases linearly so that its value after 8 years is $2,200. By what amount is the value of the equipment decreasing per year? / A. $ 275
B. $4,525
C. $4,800
D. $5,075
OGT 2006 – Problem # 22
The following table contains math contest scores of two teams in a high school math contest.
High School Math Contest Scores
Team A / Team B
90 / 87
85 / 100
87 / 87
83 / 78
80 / 78
In your Answer Document, calculate the mean and median for each team. Determine which team scored better in the contest by comparing these measures.
OGT 2005 – Problem # 19 & OGT 2004 – Problem # 31
Aaron wants the mean of his 5 geometry test
scores to be at least 90%. His scores on the first
four tests are 85%, 83%, 96%, and 91%. Which of
the following is the minimum score Aaron can
earn on the fifth test to meet his goal? / A. 89%
B. 90%
C. 95%
D. 100%
OGT 2003 – Problem #22
Consider the following scores:
12, 56, 62, 66, 74, 83, 88, 90, 93, 96
If the outlier, 12, is removed from the set
above, what is the approximate increase in the
mean of the remaining scores? / A. 3
B. 7
C. 12
D. 84
OGT 2003 – Problem #24
The mean weight of the five returning members
for Cardinal High School’s wrestling team is
168 pounds. Three freshman wrestlers joined
the team. If their weights are 140, 172 and
168 pounds, what is the mean weight of this
year’s team? / A. 160 pounds
B. 162 pounds
C. 165 pounds
D. 168 pounds

E. Evaluate the validity of claims and predictions that are based on data by examining the appropriateness of the data collection and analysis.

9.4. Describe and compare various types of studies (survey, observation, experiment), and identify possible misuses of statistical data.

OGT 2007 – Problem #34
The local newspaper publishes a list of the five most popular radio stations. Lisa’s favorite station is not on the list. At school, she asks two of her friends what their favorite station is, and they both choose Lisa’s favorite station. Based on this, Lisa decides her favorite station should have been on the list.
In your Answer Document, explain why Lisa’s conclusion is not valid by giving two reasons why her sample is biased.
OGT 2006 – Problem # 44
In 1993, the median age of brides in Ohio was 27.0 years and the median age of grooms was 28.9 years.
Based on this information, which of the following statements must be true?
A. Most brides were 27 years old.
B. The youngest groom was 28.9 years old.
C. Half of the grooms were 28.9 years old or older.
D. All the grooms were older than the brides were.
OGT 2003 – Problem #34
The graph below compares earnings categorized by level of schooling for males and females.
Which of the following statements is true based on the graph?
A. Gender does not appear to have an impact on earnings.
B. Education level does not appear to have an impact on earnings.
C. The more educated a female, the wider the earnings gap between her and her male counterpart.
D. As education level increases, the earnings gap narrows between males and females.

F. Construct convincing arguments based on analysis of data and interpretation of graphs.