Question

lesson 2: relative frequency tables
cool down: writing sample
eighty students are asked if they prefer manual or electric pencil sharpeners and if they prefer mechanical or wood pencils.

	mechanical pencils	wood pencils
electric sharpeners	34	31

1. complete the relative frequency table with the correct proportions so that it could be used to answer the following question: \among students who like manual pencil sharpeners, what proportion also prefer mechanical pencils?\

	mechanical pencils	wood pencils
electric sharpeners

1. use the table to determine the percentage of people who prefer electric sharp and wood pencils.

Explanation:

Step1: Calculate total number of students who prefer manual sharpeners

$5 + 10=15$

Step2: Calculate relative - frequency of students who prefer manual sharpeners and mechanical pencils

The number of students who prefer manual sharpeners and mechanical pencils is 5. The relative - frequency is $\frac{5}{15}=\frac{1}{3}\approx0.333$.

Step3: Calculate total number of students

$5 + 10+34 + 31 = 80$

Step4: Calculate percentage of people who prefer electric sharpeners and wood pencils

The number of students who prefer electric sharpeners and wood pencils is 31. The percentage is $\frac{31}{80}\times100\% = 38.75\%$

The relative - frequency table:

	Mechanical Pencils	Wood Pencils
Electric Sharpeners	$\frac{34}{80}=0.425$	$\frac{31}{80}=0.3875$

Answer:

1. The relative - frequency table values are as shown above.
2. $38.75\%$