To find the relative frequencies by column, calculate the ratios of each value and the total in that column.
Relative Frequencies by Column:
Number of Times Per Month
Males
Females
0 - 5
35; 0.36
25; 0.40
6 - 10
23; 0.23
16; 0.26
11 - 15
22; 0.22
13; 0.21
16 - 20
18; 0.18
8; 0.13
Total
98; 1.00
62; 1.00
Example Solution:
The relative frequency of the number of girls who bring their lunch to school less than 6 times to the total number of students is about 0.16.
We want to construct a two-way table that shows the relative frequencies by column. We also want to find the relative frequency of the number of girls who bring their lunch to school less than 6 times to the total number of students. We will do this in three steps.
Find the total number of males and the total number of females.
Construct a two-way table that shows the relative frequencies by column.
Find the relative frequency of the number of girls who bring their lunch to school less than 6 times to the total number of students.
Let's do these things one at a time.
Find the Missing Totals
Let's calculate the sum of each column to find the missing values.
Male Students:& 35+23+22+18 = 98
Female Students:& 25+16+13+8 = 62
We can add this information to the table.
Number of Times Per Month
Males
Females
0 - 5
35
25
6 - 10
23
16
11 - 15
22
13
16 - 20
18
8
Total
98
62
Construct the Table
To find the relative frequencies by column, we calculate the ratios of each value and the total in that column. We will round the results to the nearest hundredth.
Number of Times Per Month
Males
Females
0 - 5
35;35/98≈ 0.36
25;25/62≈ 0.40
6 - 10
23;23/98≈ 0.23
16;16/62≈ 0.26
11 - 15
22;22/98≈ 0.22
13;13/62≈ 0.21
16 - 20
18;18/98≈ 0.18
8;8/62≈ 0.13
Total
98;98/98=1.00
62;62/62=1.00
Looking at the relative frequencies, we can say that most of the female students bring their lunch to school between 0 and 5 times per month.
Find the Missing Relative Frequency
We want to find the relative frequency of the number of girls who bring their lunch to school less than 6 times per month to the total number of students. Let's start by looking at the given table!
Number of Times Per Month
Males
Females
0 - 5
35
25
6 - 10
23
16
11 - 15
22
13
16 - 20
18
8
Total
98
62
We can see in the table that there are 25 girls who bring their lunch to school less than 6 times per month. Now we will calculate the total number of students surveyed by Cali. To do so, we can add the number of male students and the number of female students. Let's do it!
Total Number of Students: 98+ 62= 160
Now we know that Cali surveyed 160 students in the cafeteria. To find the missing relative frequency, we will calculate the ratio of the number of girls who bring their lunch to school less than 6 times per month to the total number of students. We will round the results to the nearest hundredth.
The relative frequency of the number of girls who bring their lunch to school less than 6 times per month to the total number of students is about 0.16.
