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 sharpeners and wood pencils.

Explanation:

Step1: Calculate total number of students who prefer manual sharpeners

The number of students who prefer manual sharpeners is the sum of those who prefer manual sharpeners and mechanical pencils and those who prefer manual sharpeners and wood - pencils. So, \(5 + 10=15\).

Step2: Calculate the relative frequency for manual - sharpeners and mechanical - pencils

The proportion of students who like manual pencil sharpeners and also prefer mechanical pencils is \(\frac{5}{15}=\frac{1}{3}\approx0.333\).
For the second part:

Step3: Calculate total number of students

The total number of students is \(5 + 10+34 + 31 = 80\).

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

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

The relative - frequency table for the first part:

	Mechanical Pencils	Wood Pencils
Electric Sharpeners	\(\frac{34}{65}\)	\(\frac{31}{65}\)

Answer:

1. The relative - frequency table:

	Mechanical Pencils	Wood Pencils
Electric Sharpeners	\(\frac{34}{65}\)	\(\frac{31}{65}\)

1. \(38.75\%\)