Statistics & Probability

When you collect

information from part

of a group you are

SAMPLING the group.The group of people

from which a sample is chosen is called a

POPULATION.Did you choose enough

people for your sample?

Did the people you

chose represent the entire group?

Post - test

Sallie is going to a water park. She wants to take a survey of people at the water park to help identify the most popular water slide. She decides to ask 20 adults and 20 children at the water park’s picnic grove. Is this a good sample to use? Explain.

There are three doctor’s offices in Andre’s small town. He wants to take a survey of people in his town to help him identify which doctor he should go to for checkups. He decides to stand outside one of the doctor’s offices and ask incoming patients if they are happy with the service they receive from their doctor. Is this a good sample to use? Explain.

Post - test

How many students voted for class president?

a)20 b) 55c) 75 d) 85

Which two candidates together received 1/3 of the votes?

a)Gina & Dariob)Dario & Justinc)Gina & Justind)David & Justin

Add together the votes for Dario & David. The sum is what fraction of the total number of votes?

a)3/5 b) 1/3c) 2/5 d) 1/5

Post - test

Use the numbers from 1 to 10 to complete the Venn diagram, which shows the common factors of 18, 20, and 24.

Factors of 10 Factors of 24

Factors of 20

Step 1: List all the factors of 10.

Step 2: List all the factors of 20.

Step 3: List all the factors of 24.

Step 4: Cross out all the factors above 10.

Step 5: Circle the factors, that all three have in common and place them at the center of the diagram.

Step 6: Place the rest of the numbers in the appropriate sections.

Post - test

Consider the words HISTORY, SCIENCE, and READING. Create a Venn diagram to show which letters appear in each word. Explain your work.

In a class of 30 students, every student studies Spanish and/or French. Eighteen students study only Spanish, and 4 students study both Spanish and French. Create a Venn diagram to show the situation. How many students study only French? Explain your work.

In a seventh grade class of 25 students, 15 students own a yellow pencil. Fifteen students own a blue pencil. The same number of students own a yellow pencil or a blue pencil. Create a Venn diagram to show the situation. Explain your work. How many students own both a yellow pencil and a blue pencil?

Post - test

Another word for average is mean.

The mean or average is the sum of a group of numbers, divided by the number of addends in the group.

Mean = sum of the addends number of addends

The following is the number of problems that Ms. Mattie assigned for homework on 9 different days. What is the average number of problems she assigned per day?

8,  13,  11,  14,  9,  15,  18,  9,  11

Six earthquakes were measured using the Richter scale and their magnitudes are listed below. What is the mean?

7.9,  7.7,  8.0,  6.4,  5.4,  6.6

12

7

The mode of a set of data is the value in the set that occurs most often.

The following is the number of problems that Ms. Mattie assigned for homework on 10 different days. What is the mode?

8,  11,  9,  14,  10,  15,  18,  6,  9,  10

On a cold winter day in January, the temperature for 9 North American cities is recorded in Fahrenheit. What is the mode of these temperatures? -8,  0,  -3,  4,  -1,  0,  5,  -1,  0

Ten earthquakes were measured using the Richter scale and their magnitudes are listed below. What is the mode?

7.0,  6.2,  7.7,  8.0,  6.4,  7.2,  5.4,  6.6,  7.5,  5.9

9 and 10

0

None

The median of a set of data is the middle number in the group arranged in numerical order.

The following is the number of problems that Ms. Mattie assigned for homework on 9 different days. What is the median?

8,  11,  9,  14,  9,  15,  18,  9,  10

On a cold winter day in January, the temperature for 10 North American cities is recorded in Fahrenheit. What is the median of these temperatures? -8,  3,  -3,  4,  6,  0,  5,  -1,  0, 12

10

1.5

The range of a set of data is the difference between the highest and lowest values in the set.

The Jaeger family drove through 6 Midwestern states on their summer vacation. Gasoline prices varied from state to state. What is the range of gasoline prices?

$1.79,  $1.61,  $1.96,  $2.09,  $1.84,  $1.75

A marathon race was completed by 5 participants. What is the range of times given in hours below?

2.7 hr,  8.3 hr,  3.5 hr,  5.1 hr,  4.9 hr

$0.48

5.6 hr

A pictograph is best used when comparing how many times a

data value occurs.

A bar graph is usually used to compare

numbers of amounts in categories.

A line graph is used to show

how data changes over

time.

A histogram shows data grouped in equal intervals.

A circle graph is best

used for comparing part of a group to

another part of a group or to the whole.

Post - test

Which percent best represents the strings section?

a) 90% b) 60% c) 70% d) 30%

Approximately what percent of the orchestra are percussion instruments?

a) 20% b) 25% c) 8% d) 1%

What is the range of temperatures in the graph shown above? Show and explain all work.

The following tally chart shows the favorite sports of all the students in the 5th grade class.

What sports are the most popular in the 5th grade?

How many students are in in the 5th grade?

Color Tally

Basketball 1111 1111

Baseball 1111 1111

Football 1111 1

Tennis 111

Swimming 1111 111

Track 11

Grades on the Math test

X

X

X

X

X

X

X

X

X

X

X

X

X

XX

75 80 85 90 95 100

How many students scored above an 85 on the math test?

What is the most common grade on this math test?

How many students took the math test?

Is the median test grade the same as the mode test grade?

Stem Leaf

0

1

2

3

4

5

6

8 8 9

9

0 0 2 4 4 8 9

1 1 2 4 5 5 6 6 7 7 8

0 0 0 3 8 9

2 4

1

How many members are on the chess team?

Matches won by each member of the Avery Middle School Chess Team

What is the range of the number of matches won?

Find the mean, median, and mode for these data.

1 | 9 = 19

Animal Species in Zoos

0 100 200 300 400 500 600 700 800

Los Angeles

Lincoln Park

Cincinnati

Bronx

Oklahoma City

Zo

o

Species

Which zoological park has the most species?

What is the range of the animals in the zoological parks?

How many presidents were younger than 50 when they were inaugurated?

Susan took a survey of 75 students in two classes at her school to find out if they favored lemonade over water. Fifty students said they favored lemonade over water. There are 600 students at Susan’s school. How can you predict the total number of students who favor lemonade over water at Susan’s school?

Step 1: Find the ratio of students surveyed who favor lemonade over water50 / 75

Step 2: Use the ratio to write a proportionLemonade / Total 50 / 75 = n / 600

Step 3: Solve the proportion75n = 30,000n = 400

Step 4: So a good prediction for the number of students who favor lemonade over water is

400 students

List all the possible outcomes of rolling the die and spinning the spinner.

Step 1: List the possible outcomes of rolling the die.1, 2, 3, 4, 5, 6 - 6 possible outcomes

Step 2: List the possible outcomes of spinning the spinnerRed, Blue, Green - 3 possible outcomes

Step 3: Make a tree diagram to show all the possible outcomes

Step 4: Trace each path to list the possible outcomes.R1, R2, R3, R4, R5, R6, B1, B2, B3, B4, B5, B6, G1, G2, G3, G4, G5, G6 There are 18

possible outcomes

List all the possible outcomes for tossing a nickel, a dime, and a quarter.

How many outcomes are there for rolling a standard number cube and tossing a dime?

List the outcomes for tossing two number cubes each with faces numbered from 1 through 6.

Valerie designed an experiment consisting of rolling a number cube with faces numbered 1 through 6, tossing a penny, and tossing a nickel. List the outcomes for Valerie’s experiment. Explain your answer.

Determine the probability of rolling a ‘5’ and spinning a ‘Red’.

Step 1: Determine the probability of rolling a ‘5’P(5) = 1/6

Step 2: Determine the probability of spinning a ‘Red’P(Red) = 2/6 or 1/3

Step 3: Determine the probability of rolling a 5 and spinning a Red

P(5 and Red): 1/6 * 1/3 = 1/18Step 4: You can make a tree diagram to check your answer.

A box contains 2 oatmeal, 3 strawberry, and 6 cinnamon snack bars. Ruby reaches in and grabs a bar. She reaches in again and grabs another bar. Find the probability that she will choose a cinnamon bar and then a strawberry bar?

A red and blue number cube are rolled. Find the probability that an odd number is rolled on the red cube and a number greater than 1 is rolled on the blue cube.

A standard deck of playing cards contains 52 cards in four suits of 13 cards each. Two suits are red and 2 suits are black. Two cards are chosen from the deck one after another. Find each probability.

P(2 hearts) P(red, black)

A spinner is spun and a die is rolled at the same time. How many possible outcomes are there?

Step 1: Possible outcomes of rolling the die6

Step 2: Possible outcomes of spinning the spinner3

Step 3: Apply the Fundamental Counting Principle6 * 3 = 18 possible outcomes

Step 4: You can make a tree diagram to check your answer.

Nick wants to create a secret code word that consists of 4 letters. How many different combinations are possible if letters can be repeated?

The code for Maria’s garage door opener has 3 digits. The possible digits are 0 – 9. The digits can be repeated. How many different codes are possible?

How many ways can you arrange the letters A, B, C, D in a row?

Everyone in the company where Josephine works wears an identification badge with 3 letters that are vowels followed by 2 digits that are odd. Letters and digits can be repeated. How many different badges are possible. Show and explain all work.