Grade 7 Practice Problems: Data, Statistics & Probability
Examples from Standards Revision and GLEs
7D-20) Answer: 23
Irving the Invisible is beginning to reappear! Help! He desperately needs more of his invisibility potion. He must drink two gallons of the potion to remain invisible for the next 24 hours. Once opened, Irving must drink the full bottle. He has 24-ounce, 32-ounce, 48-ounce, and 64-ounce bottles of the liquid. How many different combinations of bottles can you find which Irving can drink to prevent his reappearance? (There are 128 ounces in a gallon) Explain in detail how you found your answer using words, numbers, and/or pictures.
7D-19) Answer: 68
"Well," says Mrs. Garcia, "raccoons got into the garbage can again last night, and now there is trash all over the yard!" Antonio and Maria look at each other and quickly say in the same breath, "I cleaned it up last time!" Mrs. Gomez proposes a game to decide who will clean up the yard. She hands Antonio a special die from one of the family board games. The six sides of the die are marked 11,10, 9, 8, 7, and 6. The object of the game is to roll the die four times. The first person to make a total of 30 in four rolls of the die does NOT have to clean the yard. How many different ways can the die be rolled four times and make a total of 30 points exactly? Explain in detail how you found your answer using words, numbers, and/or pictures.
7D-18) Answer: 70
Jacob's home town is celebrating its 100th anniversary. Jacob's father, who is an electrician, is preparing to wire the belltower in the town square with lights. Jacob's father decides he will need 90 feet of lights to dramatically light up the tower. The lights come in strings with lengths of 60 feet, 50 feet, 30 feet, 20 feet, 10 feet, and 5 feet. How many combinations of lights can you find that Jacob's father could use for the tower? Explain in detail how you found your answer using words, numbers, and/or pictures.
7D-17) Answer: 89
Pablo spent the entire day on the roller coaster at Four Flags Amusement Park. As he finally left the park, just before closing time, he saw a huge, lime-green dinosaur at the Ring-Toss Booth. He knew it would be the perfect birthday present for his little sister. "Wait a minute," he said to his friends, "I have to win this for Oriana." His friends watched as Pablo was given four rings to toss. He aimed each ring at six pins labeled 25, 20,10, 8, 5, and 0. The person in the booth explained, "You must toss all four rings, and your total must be 40 points to take the prize dinosaur." How many different ways could Pablo toss the rings and win the dinosaur? Explain in detail how you found your answer using words, numbers, and/or pictures.
7D-16) Answer: 25 different two-digit numerals
The Clinton School is putting numbers on the new basketball jerseys. Players must choose two numbers from the set of 1, 3, 5, 7 and 9. How many different two-digit numerals can they make? What if they might also select a one-digit numeral? Explain in detail how you found your answer using words, numbers, and/or pictures.
7D-15) Answer: 66 games
The Continental Hockey League consists of two conferences, each with six teams. Every team plays the teams within its own conference twice and plays each team in the other conference once. How many games are played during the season? Explain in detail how you found your answer using words, numbers, and/or pictures.
7D-14) Answer: 49 license plates
Bikeport uses license plates for its motorcycles. Each license plate consists of one vowel followed by one digit. There are 5 possible vowels and 10 possible digits. Since the zero and capital 0 look the same, they cannot be used together. How many different license plates are possible? Explain in detail how you found your answer using words, numbers, and/or pictures.
7D-13) Answer: 10
It's Party Day at the zoo. Gina and her friends each have three tickets, so they are trying to decide what three activities they want to do. They could enter a costume contest, watch a monkey show, go through a hunted house, watch a play, or go on a hay ride. How many different combinations of three activities they could choose? Explain in detail how you found your answer using words, numbers, and/or pictures.
7D-12) Answer: 10 before shelving, and 14 more after shelving; for about an .8% total
It's true: The odds of finding a cracked egg in a shipment of eggs is 1 egg in 24 cartons before those cartons are placed on grocery store shelves. Once they are on shelves, however, your odds of getting a cracked egg rise to 1 egg in every 10 cartons. Each carton holds a dozen eggs. How many cracked eggs can a grocery expect to find a shipment of 2,880 eggs just off the truck? How many more of these eggs will be cracked after being put on shelves? About what percent of the total shipment of eggs will be broken? Explain in detail how you found your answer using words, numbers, and/or pictures.
7D-11) Answer: 256
Laura is training her pet white rabbit, Ghost, to climb up a flight of 10 steps. Ghost can only hop up 1 or 2 steps each time he hops. He never hops down, only up. How many different ways can Ghost hop up the flight of 10 steps? Explain in detail how you found your answer using words, numbers, and/or pictures.
7D-10) Answer: The odds are 2/5 that the tiles will match. It is not a fair game.
Nick and Jenny are playing a game. There are six tiles in a box: three red and three blue. A player picks two tiles without looking. Jenny gets a point if the tiles don't match; Nick gets a point if they do match. What are the odds that both tiles will have the same color? Is this a fair game? Explain in detail how you found your answer using words, numbers, and/or pictures.
7D-9) Answer: 14 2/5 miles per hour
Sam is riding a bicycle race. Two thirds of the course runs uphill. One third runs downhill. When Sam is riding uphill, he rides at an average speed of 12 miles per hour. When he rides downhill, he rides at an average speed of 24 miles per hour. What is his average speed for the whole course? Explain in detail how you found your answer using words, numbers, and/or pictures.
7D-8) The 24-member Student Council is trying to decide how the school should use the available money to celebrate the beginning of summer: Six members want to hold a school dance. Five members want to have an old-fashioned barbecue. Four members want to buy an all-school pass to the amusement center. Five members want to hold a carnival. Four members want to divide the money up equally among the classes and let each class sponsor decide. Express this information in three different graphical forms. Explain in detail how you found your answer using words, numbers, and/or pictures.
7D-7) Answer: 120 ways
The Booster Club has designed five school-spirit flags that can be waved during sporting events. How many different ways can the flags be arranged along the sidelines Explain in detail how you found your answer using words, numbers, and/or pictures.
7D-6) Answer: 54 chocolate, 1 white
There are 55 containers of milk in the school refrigerator. Some are chocolate milk and some are white milk. If you select any 2 containers without looking at them, at least 1 of them will be chocolate milk. How many of each kind of milk are there in the refrigerator? Explain in detail how you found your answer using words, numbers, and/or pictures.
7D-5) Answer: ½ for one person; ¼ for 2 people; 1/8 for 3 people; 1/16 for 4 people; this will never be identically zero
What are the odds that flipping a coin will result in heads? What are the odds that two students, each flipping a coin, will both get head? What are the odds that three students, each flipping a coin, will all get heads? What are the odds that four students, each flipping a coin, will get heads? Will you ever reach the point where it is impossible for a group of students, each flipping a coin, to get head? Explain in detail how you found your answer using words, numbers, and/or pictures.
7D-4) Answer: 1/39
You have been asked to watch all of 20 kindergarten students at Monroe on the playground. Before you can stop them, every one of them throws their shoes down the storm drain where you can't see them. Using a stick, you can pull one shoe out one at a time. What are the odds that the second shoe you pull up will match the first? Explain in detail how you found your answer using words, numbers, and/or pictures.
7D-3) Answer: 3/10
All of the numbers from 1 to 50 are written on ping pong balls and put into a box. What is the probability of drawing a prime number from the box? Explain in detail how you found your answer using words, numbers, and/or pictures.
7D-2) Answer: one of each has a probability of ¼, while 2 of the same has a probability of 9/38
Chancy the Clown is giving out pogs and ride tokens at the county fair. There are 10 pogs and 10 ride tokens in her pocket. If Chancy pulls two prizes out of her pocket, are they most likely to be two pogs, two tokens, or one of each? Explain in detail how you found your answer using words, numbers, and/or pictures.
7D-1) The tour partners need to rent a truck to transport camping gear, clothes, and bicycle repair equipment. They checked prices at two truck rental companies. East Coast Trucks charges $4.25 for each mile a truck is driven. Make a table of the charges for 0, 25,50, 75, 100,125,150,175, 200, 225, 250, 275, and 300 miles. Philadelphia Truck Rental charges $200 for a week, or any part of a week, and an additional $2.00 for each mile a truck is driven. Make a table of the charges for renting a truck for five days and driving it 0, 25, 50, 75,100,125, 150,175, 200, 225, 250, 275, and 300 miles. On one coordinate grid, plot the charge plans for both rental companies. Use a different color to mark each company's plan. Which truck rental company do you think would be the best deal for the partners?
A camping-supply store rents camping gear for $25 per person. Using increments of 5 campers, make a table showing the total rental charge for 0 to 50 campers. Make a coordinate graph of these data. Compare the pattern of change in your table and graph with patterns you found in the campground fee data in question 1. Describe the similarities and differences between the two sets of data.
This table shows the fees charged for campsites at one of the campgrounds on the Ocean and History Bike Tour:
Number of campsites |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
Total campground fee |
$12.50 |
$25 |
$37.50 |
$50 |
$62.50 |
$75 |
$87.50 |
$100 |
Make a coordinate graph of these data. Would it make sense to connect the points on your graph? Why or why not? Using the table, describe the pattern of change you find in the total campground fee as the number of campsites needed increases. How is this pattern shown in your graph? Explain in detail how you found your answer using words, numbers, and/or pictures.
YEAR |
NAME |
TIME (SECONDS) |
1964 |
Celia Cuthbert, AUS |
52.0 |
1968 |
Colette Besson, FRA |
52.0 |
1972 |
Monika Zehrt, F, GER |
51.08 |
1976 |
Irena Szewinska, POL |
49.29 |
1980 |
Marita Koch, F. GER |
48.88 |
1984 |
Valerie Brisco-Hooks, USA |
48.83 |
1988 |
Olga Bryzguina, USSR |
48.65 |
1992 |
Marie-Jose Perec, FRA |
48.83 |
Make a coordinate graph of the (year, time) information given in the table. Be sure to choose a scale that allows you to see the differences between the winning times. What patterns do you see in the table and graph? For example, do the winning times seem to be rising or falling? In which year was the best time earned?
Katrina's parents kept a record of her growth from her birth until her eighteenth birthday Their data is shown in the table below
Age |
Birth |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
Height |
20 |
29 |
33.5 |
37 |
39.5 |
42 |
45.5 |
47 |
49 |
52 |
54 |
56.5 |
59 |
61 |
64 |
64 |
64 |
64 |
Make a coordinate graph of Katrina's height data. During which time interval(s) did Katrina have her largest "growth spurt"? During which time interval(s) did Katrina's height change the least? Would it make sense to connect the points on the graph? Why or why not? Explain in detail how you found your answer using words, numbers, and/or pictures.
Represent the sample space of experiments in multiple ways, including tree diagrams or organized lists, and find the theoretical probability of a particular event. The sample space represents the set of all possible outcomes. Example:
Use theoretical probability to evaluate or predict experimental outcomes Represent the probability of a particular event using fractions, decimals, and percents. Use area models to determine probability. Example:
Design a simulation for a problem situation, use the simulation to find probabilities, and explain why the simulation is a good model of the situation. Explain what happens to the mean of a data set when there is a change in the magnitude or number of data values, or both. Example:
Create data sets for a given mean, median, mode, or range. Create and interpret histograms, stem-and- leaf plots, line plots, circle graphs, and box-and-whisker plots to represent data and support conclusions. |
Examples of Probability and Statistics from the 2006 GLEs – Grade 7
Determine and explain when events are mutually exclusive. Determine and explain when events are complementary. Identify or explain when events are complementary, mutually exclusive, or neither. Represent the probability of an event given the probability of its complement. Determine the probabilities of complementary or mutually exclusive outcomes or events. Revise a game with unequal probabilities for all players and makes it a fair game. Determine, interpret, or express probabilities in the form of a fraction, decimal, or percent. Predict the probability of outcomes of experiments and tests the predictions. Predict the probability of future events based on empirical data. Count and/or list the sample space of mutually exclusive and complementary events. Formulate a question or survey that will obtain appropriate information while avoiding bias. Identify a population sample, and collects data from the selected population for an intended purpose. Describe how a question, collection method, or population may affect the data. Determine whether collected data provides useful information for the stated purpose. Describe how to collect data about a given population. Explain the effects of extreme values on the mean of a set of data. Describe how additional data added to data sets may affect the measures of central tendency. Explain the relationship between the range and measures of central tendency. Complete a set of data based on a given mean, median, or mode and a partial set of data. Explain why the mean, median, and mode may not be the same and what each indicates as a measure of central tendency in a given situation. Determine and/or use the mean, median, mode, and/or range for a set of data. Describe the accuracy and completeness of the data in a Venn diagram, stem and leaf plot, box and whisker plot, and/or scatter plot. Read and interpret the data in Venn Diagrams, stem and leaf plots, box and whisker plots, and/or scatter plots. Select and explain which graph type is the most appropriate representation for a given set of data. Interpret and describe trends and patterns represented in data and data displays. Explain statistical information, including median, range, inter quartile range, for a given box and whisker plot. Use data from a sample or data display to make an inference. Explain how the same set of data can support different points of view. Explain how data have been used or misused to support a point of view. |