1. Two Way Frequency Tables

2. Two Way Frequency Tables
Two-way frequency tables are used to examine the relationships between two ________________variables.
The table below is an example of a two-way frequency table that shows the number of students who prefer art, band, or chorus at Clayton High School.
categorical

3. Joint Frequency
Joint
___________ frequency represents the intersection of one row variable and one column variable
The following questions are examples of joint frequency:
How many 11th graders prefer chorus?
How many 12th graders prefer art?
How many 9th graders prefer band? 32 25 22

4. Marginal Frequency Marginal adding
___________ frequency represents the total of a row or column
If the table does not include a total row/column, it is often helpful to make one by ____________ straight down and straight across
Remember the horizontal total and vertical total should be the same
Complete the table below so that it included marginal frequencies
adding
Band
Chorus
Art Club
Total
9th Grade 22 30 26
10th Grade 25 24
11th Grade 31 32 20
12th Grade 28 17 78 71 83 70
106
101 95
302

5. Marginal Frequency 70 95 band 12th grade
The following questions are examples of marginal frequencies:
What is the marginal frequency of 12th graders?
What is the marginal frequency of students who prefer art?
Which subject has the highest marginal frequency?
Which grade level has the lowest marginal frequency? 70 95
band
12th grade
Band
Chorus
Art Club
Total
9th Grade 22 30 26 78
10th Grade 25 24 71
11th Grade 31 32 20 83
12th Grade 28 17 70
106
101 95
302

6. Conditional Frequency
Conditional probability is the probability of an event occuring, given that another event has ______________________.
To find conditional probability, you divide the ____________probability where both conditions are met by the ______________probability of the event that has already occurred or must be true.
already occurred
joint
marginal
Band
Chorus
Art Club
Total
9th Grade 22 30 26 78
10th Grade 25 24 71
11th Grade 31 32 20 83
12th Grade 28 17 70
106
101 95
302

7. Conditional Frequency
What is the probability that a student in band is in 11th grade?
Given that a student is in 9th grade, what is the probability that they’re in chorus?
What is the conditional frequency that an art club student is in 11th or 12th grade?
𝟑𝟏 𝟏𝟎𝟔
𝟑𝟎 𝟕𝟖
𝟒𝟓 𝟗𝟓
Band
Chorus
Art Club
Total
9th Grade 22 30 26 78
10th Grade 25 24 71
11th Grade 31 32 20 83
12th Grade 28 17 70
106
101 95
302

8. Conditional Frequency/Percent
Questions about two-way frequency tables will often ask you to express an answer as a ______________
Percentages can be found in the same way as __________________
Percent =
Remember that two-way frequency tables don’t always include _________ and it may be necessary to find these when finding percentages
𝐩𝐞𝐫𝐜𝐞𝐧𝐭
𝐩𝐫𝐨𝐛𝐚𝐛𝐢𝐥𝐢𝐭𝐢𝐞𝐬
𝐩𝐚𝐫𝐭 𝐨𝐟 𝐢𝐧𝐭𝐞𝐫𝐞𝐬𝐭 𝐰𝐡𝐨𝐥𝐞 𝐠𝐫𝐨𝐮𝐩 𝐨𝐟 𝐢𝐧𝐭𝐞𝐫𝐞𝐬𝐭 𝐱𝟏𝟎𝟎
𝐭𝐨𝐭𝐚𝐥𝐬

9. The two way frequency table below shows the gender and preferred subject of 99 high school students. Use this table to answer the questions below. Round each answer to the nearest percent.
What percentage of students who prefer a foreign language are female?
What percentage of male students prefer language arts?
What percentage of students who prefer science are male?
What percentage of female students prefer math? 𝟏𝟏 =
.𝟑𝟑𝟑=
𝟑𝟑% 𝟑𝟑 𝟐𝟐 =
.𝟒𝟒𝟖=
𝟒𝟓% 49 𝟏𝟐 =
.𝟑𝟑𝟑=
𝟑𝟑% 𝟑𝟔 𝟏𝟓 =
.𝟑=
𝟑𝟎% 𝟓𝟎

10. Relative Frequency Tables
𝐑𝐞𝐥𝐚𝐭𝐢𝐯𝐞
____________ frequency tables display the data from frequency tables, relative to the total
To find relative frequency, take the number in each box and divide it by the ______
Create a relative frequency to display the data in the table below. Since the total number of people surveyed here is _____, divide each box by _____.
𝐭𝐨𝐭𝐚𝐥 𝟓𝟎 𝟓𝟎
Gender
Preferred Program
Dance
Sports
Movies
Total
Women
Men
.𝟑𝟐
.𝟏𝟐
.𝟏𝟔
.𝟔𝟎
.𝟎𝟒
.𝟐𝟎
.𝟏𝟔
.𝟒𝟎
.𝟑𝟔
.𝟑𝟐
.𝟑𝟐
𝟏.𝟎𝟎

11. Relative Frequency Tables
You can find conditional probabilities from a relative frequency table the same way you found them with your two way frequency table
Set up the proportions in the same way with _____________ instead of the whole numbers
If you’re asked to find a total number of people when you are given the relative frequency table (with decimals), work backwards by ________________ the relative frequency by the __________ number of people surveyed
𝐝𝐞𝐜𝐢𝐦𝐚𝐥𝐬
𝐦𝐮𝐥𝐭𝐢𝐩𝐥𝐲𝐢𝐧𝐠
𝐭𝐨𝐭𝐚𝐥

12. The relative frequency table below shows the number of sports male and female students play. Use this frequency table to answer each question below.
Given that a student is a female, what is the probability that she plays 2 sports?
What percentage of students who played three sports were male?
What is the probability that a female student plays no sports?
If 300 students were surveyed, how many males played 1 sport?
If 200 students were surveyed, how many females played 2 sports?
.18 =
.𝟑𝟖
.𝟏𝟐 =
.𝟕𝟓=
𝟕𝟓%
.16
.𝟎𝟑 =
.𝟑𝟖
𝟑𝟎𝟎∙(.𝟏𝟒)= 𝟒𝟐
𝟐𝟎𝟎∙(.𝟏𝟖)= 36

13. Independent and Dependent Evens

14. Independent and Dependent Events
𝐢𝐧𝐝𝐞𝐩𝐞𝐧𝐝𝐞𝐧𝐭
𝐢𝐬 𝐧𝐨𝐭
Two events are _____________________ if the result of the 2nd event ________ affected by the result of the first event. 
Ex: A box contains 4 red, 3 green, and 2 blue marbles. One marble is removed and then replaced. Another marble is drawn. What is the probability that the first marble is blue and the second marble is green?
Because the marble is replaced the ___________________ does not change. It stays _____ marbles.
Two events are _________________ if the result of the first event _________________ the outcome of the second event so that the probability is changed. 
Ex: A box contains 4 red, 3 green, and 2 blue marbles. One marble is removed, but not replaced. Another marble is drawn. What is the probability that the first marble is blue and the second marble is green?
Because the marble is not replaced the ___________________ does change from _____ to _____ marbles.
𝐬𝐚𝐦𝐩𝐥𝐞 𝐬𝐩𝐚𝐜𝐞 𝟗
𝐝𝐞𝐩𝐞𝐧𝐝𝐞𝐧𝐭
𝐝𝐨𝐞𝐬 𝐚𝐟𝐟𝐞𝐜𝐭
𝐬𝐚𝐦𝐩𝐥𝐞 𝐬𝐩𝐚𝐜𝐞 𝟗 𝟖

15. Decide if each set of events below represent independent or dependent events.
You flip a coin and then roll a fair six-sided die. The coin lands heads-up and the die shows a one.
A box of chocolates contains five milk chocolates, five dark chocolates, and five white chocolates. You randomly select and eat three chocolates. The first piece is milk chocolate, the second is dark chocolate, and the third is white chocolate.
A cooler contains ten bottles of sports drink: four lemon-lime flavored, three orange flavored, and three fruit-punch flavored. Three times, you randomly grab a bottle, return the bottle to the cooler, and then mix up the bottles. The first time, you get a lemon-lime drink. The second and third times, you get fruit- punch.
A bag contains eight red marbles and four blue marbles. You randomly pick a marble and then pick a second marble without returning the marbles to the bag. The first marble is red and the second marble is blue.
INDEPENDENT OR DEPENDENT

16. Decide if each set of events below represent independent or dependent events.
A bag contains four red marbles and six blue marbles. You randomly pick a marble and then return it to the bag before picking another marble.
You roll a fair six-sided die three times. The die shows an even number every time.
There are eight nickels and eight dimes in your pocket. You randomly pick a coin out of your pocket and place it on a counter. Then you randomly pick another coin. Both coins are nickels.
You flip a coin twice. The first flip lands heads-up and the second flip lands tails-up
INDEPENDENT OR DEPENDENT