Number System Cumulative Review

Number System Cumulative Review

1. Cicadas spend most of their lives underground and only emerge every 13 or 17 years depending on the brood. If both types of cicadas appeared this year, then in how many years will the 13-year and 17-year cicadas appear again in the same year?
2. Find the mean, median, and mode of the data set: 16, 21, 11, 34, 26, 12, 31, 11, 17, 21. Identify the values that would change if “31” is added to the set.
3. Joanna wants to buy a gift basket for each of her subject teachers. Each basket has 7 pieces of fruit and 3 types of chocolate. She has 6 teachers. How much food will they receive altogether? Write the problem in two different ways. Solve the problem.
4. Morris is an amateur skateboarder and has won many competitions. His highest scores in the past few competitions were 390, 364, 349, and 380. He needs an average score of 372 in order to be considered as a professional skateboarder. What score will he need in order to have an average high score of 372?
5. Jonathan has 200 baseball cards. He has more baseball cards than Malik. How many baseball cards does Malik have?
6. For science class, Hoyt had to collect information about the number of pets people have in their households. Hoyt asked 6 of his friends and created the dot plot below.

Number of Pets

xx

xxxx

012345678910

1. Find the mean, median, and mode for the data.
2. Find a data set of six numbers that has the same mean as Hoyt’s data.

1. Jordan bought new clothes with money he received for his birthday. The total of items before sales tax is $128.25. Sales tax is calculated by multiplying the total amount by 0.07. How much tax will Jordan pay for his new clothes? Round your answer to the nearest hundredth. How much is his total with tax?
2. Philip surveyed his friends about how many hours of T.V. they watched last week. The following numbers are how many hours each friend had watched: 3, 3, 3, 5, 6, 7, 11, 15, 16, and 18. Use the data to answer the following questions.

1. How many friends did he survey?
2. What is the total number of hours all his friends watched?
3. What is the mean number of hours they watched T.V.?
4. Create a box-and-whisker plot for the data.
5. Philip asked eight of his classmates the same question and added it to his data set. His classmates watched T.V. for the following number of hours: 2, 2, 4, 4, 4, 5, 5, and 5. Write the new data set in order from least to greatest to include his classmates.
6. Create a box-and-whisker plot for the new data set.
7. Compare the two box-and-whisker-plots. What do you notice? Explain.

1. Joyce spends $1,289.76 per month on rent and supplies for her nail salon. If she charges $12.50 for a manicure, how many manicures must Joyce do to cover her monthly expenses?
2. Ashli wants to figure out what grade she is getting in Social Studies. Her test scores this marking period were 85.6, 78.25, 91.5, 73, and 84.9. What was her average test score? Round your answer to the nearest whole number.
3. There are 30 students in the classroom. If three groups of 4 students leave the room, how many are left? Write a numerical expression to represent the situation. Solve your expression.
4. Fitness trainer Donna makes a healthy juice mix for her clients. She uses cup of orange juice, cup of pineapple juice, cup of carrot juice, cup of wheat grass and cup of apple juice for one batch of her juice mix. How cups are in one batch? How many ounces?

1. Mr. Thomas’ science class planted beans in clay pots. The students recorded the growth of each plant once a week, after the plants sprouted, in the following chart:

a) What is the average growth per week of group A’s plant? Group B’s plant? Group C’s plant?

b) What is the median of Group A’s data? Group B’s data? Group C’s data?

c) What is the mode of the entire data set?

1. Savannah is making costumes for this year’s parade. The pattern she is using calls for 2.875 yards of fabric for each costume. How many yards of fabric will she need to make 38 costumes?
2. Larry surveyed his friends about how many movies they watched last month. He created the box-and-whisker plot below to show his data.

Number of Movies Watched

1. What is the minimum number of movies watched?
2. What is the maximum number of movies watched?
3. What is the median value of the data?
4. What percent of his friends watched 15 movies or more?
5. What percent of his friends watched between 4 and 15 movies?
6. What percent of his friends watched 4 movies or more?

1. Annabel’s family loves collecting fitted baseball caps. She wrote down the cap size for each family member so that she can buy each person a new cap before baseball season starts. She will need to buy the following sizes: , , , and . What is the average cap size for her family?
2. Matthew goes hiking every 12 days and swimming every 15 days. He did both kinds of exercise today. How many days from now will he go both hiking and swimming again? How many times will he have gone hiking? How many times will he have gone swimming?
3. Abigail scored an 86, 91, 77, 98, and a 100 on her last 5 social studies tests. She needs an average of 90 in order to make honor roll this marking period. What score does she need on her last test in order to have a mean score of 90 in this class? In order to make high honor roll, students must have an average of 95 or higher. What score would Abigail need on her last test to achieve high honor roll?
4. A group of seven friends find they have a mean of 3 video games per household. Find a data set that fits this description. Then make a dot plot for this data.
5. An isosceles triangle has a perimeter of 12.8 mm. The two congruent sides measure 4.093 mm each. What is the length of the third side?
6. Mrs. Wayne’s class had a hula hoop competition. They recorded how many times each student spun the hula hoop without stopping or dropping the hula hoop.

Hula Hoop Spins

Use the data to find the following:

1. Minimum
2. Maximum
3. Range
4. Lower Quartile
5. Median
6. Upper Quartile
7. Interquartile Range
8. Outlier(s)

1. What number is one-hundredth of the number shown in expanded form below?

5(100) + 2(10) + 3(1) + 6(1/10) + 0(1/100) + 9(1/1000)

1. Joanne is campaigning for class president and plans to distribute some campaign materials: 30 flyers and 45 buttons. She wants each classroom to receive an identical set of campaign materials, without having any materials left over. What is the greatest number of classrooms Joanne can distribute materials to? How many flyers and how many buttons will each classroom receive?

1. Mrs. Riley’s class recorded how many jumps each student could jump rope without stopping. Create a frequency table and a histogram for the data.

Number of Jumps

1. The shortest side of a right triangle measures 4.18 mm. The adjacent side, the side that creates the right angle, measures 12.9 mm. The hypotenuse measures 13.5511 mm. What is the perimeter of the triangle?

1. The Speedster roller coaster has a speed of miles per hour and the Mini Monster roller coaster has a speed of 53 miles per hour. How much faster is the Speedster roller coaster than the Mini Monster?
2. The pet store has 9 fish bowls for sale. Each fish bowl contains 3 clownfish and 2 starfish. How many fish are they selling in all? Write the problem in two different ways. Solve the problem.

1. Mr. Sampson’s class took a survey of how many siblings each student has and created the dot plot shown below.
2. How many students are in Mr. Sampson’s class?
3. Determine the mean, median, and mode for the data.

Number of Siblings

xx

xxx

xxx

xxxxx

xxxxxxx

012345678910

1. At the Bake Shop, they sell cheesecakes for $12 each. You can buy any fractional part of a cheesecake and pay that fraction of $12. A customer purchased of a cheesecake. Mrs. Johnson asks to buy of the remaining cheesecake. What fraction of a whole cheesecake does Mrs. Johnson buy? What does she pay?
2. There are a total of 1,560 students, grades K-12, in the town of Little River, NY. If each class has 24 students, how many classes are there?
3. Dr. Parker is a pediatrician and wants to compare the heights of his sixth grade patients with the heights of his fifth grade patients. Use the data below to create a two separate dot plots for each of the groups of patients.

Height of Sixth Graders (in inches)

Height of Fifth Graders (in inches)

Use the dot plots to answer the following questions:

1. How many of Dr. Parker’s patients are in sixth grade?
2. How many of Dr. Parker’s patients are in fifth grade?
3. Analyze the distribution of the data in the dot plots and explain which data set you think has the larger mean value.
4. Determine the mean, median, and mode for each of the data sets.
5. Compare the mean values for both data sets. How do the mean values relate to the distribution of the dot plots?
6. Find the mean absolute deviation for each of the data sets.

1. Marquette, Michigan receives (12,920  102) inches of snow each year. Evaluate the expression to find the annual snowfall. Convert your answer to feet and round your answer to the nearest thousandths.

1. The ink cartridge shown below can be refilled with a maximum of how much ink?

1. Noel is a Girl Scout Leader and just finished organizing the data of their most recent cookie sales. She created the following histogram to show how many boxes each customer purchased.

Girl Scout Cookie Sales

Number of Boxes

1. How many customers purchased between 21 and 25 boxes of cookies?
2. How many customers purchased between 6 and 10 boxes of cookies?
3. Which measure(s) of center (mean, median, or mode) appropriately represents the data? Why?
4. Can you determine if the mean or median is greater? If yes, which is greater and why? If not, why are you unable to determine the greater value?

Answer Key

1. 221 years
2. Mean – 20; Median – 19; Mode – 11 and 21; All three change.
3. 6(7 + 3)6 x 7 + 6 x 360
4. 377
5. 160 baseball cards
6. Mean – 4; Median – 3.5; Mode – 3 and 6
7. Answers will vary
8. $8.98; $137.23
9. 10
10. 87
11. 8.7

1. 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5, 6, 7, 11, 15, 16

1. The second box-and-whisker plot is skewed to the left because most of the data lies between 2 and 7.

1. 104 manicures
2. 82.65
3. ; 18 students
4. cups; ounces
5. Group A – 1.21 cm; Group B – 1.088 cm; Group C – 0.95 cm
6. Group A – 1.2 cm; Group B – 1.2 cm; Group C – 0.95 cm
7. 1.2 cm
8. 109.25 yd

NJ Center for Teaching and Learning ~ 1 ~

1. 4
2. 18
3. 10.5
4. 25%
5. 50%
6. 75%

NJ Center for Teaching and Learning ~ 1 ~

1. 7
2. 60 days, hiking 5 times, swimming 4 times
3. 88; 118
4. Answers will vary
5. 4.614 mm

NJ Center for Teaching and Learning ~ 1 ~

1. 1
2. 92
3. 91
4. 11
5. 23
6. 50
7. 39
8. 92

NJ Center for Teaching and Learning ~ 1 ~

1. 5.23609
2. 15 classrooms, 2 flyers, 3 buttons
3. Frequency Table

Jump Rope

1. 30.6311 mm
2. miles per hour
3. 9(3 + 2)9 x 3 + 9 x 245
4. 20
5. Mean – 2.45; Median – 2; Mode – 1 and 2
6. , $4
7. 65 classes

Sixth Grade Patients

x

xx

xxxxxx

xxxxxxxxxxx

50515253545556575859606162636465

Height in Inches

Fifth Grade Patients

x

xxx

xxxxx

xxxxxxxxxxx

50515253545556575859606162636465

Height in Inches

1. 20
2. 20
3. Sixth Grade data has the larger mean value. Explanations will vary.
4. Sixth Grade: Mean – 60.1; Median – 61; Mode – 62

Fifth Grade: Mean – 56.15; Median – 56; Mode – 56

1. Answers will vary
2. Sixth Grade mean absolute deviation – 2.69

Fifth Grade mean absolute deviation – 2.58

1. 129.2 inches; 10.767 feet
2. 186 cubic centimeters
3. 10
4. 30
5. Answers will vary

NJ Center for Teaching and Learning ~ 1 ~