Question

a researcher gathered data on hours of video games played by school - aged children and young adults. she collected the following data:
(a) complete the frequency distribution for the data.

Explanation:

Step1: Count the total number of data points

First, count all the data points in the given table. There are \(10 + 10+10 + 8=38\) data points.

Step2: Count the frequency for each interval

• For \(0 - 2\):

Count the numbers \(0,1,2\) in the data set. The values are \(1,0,2,2,1,2,0,1,2\). So the frequency \(f_{0 - 2}=9\).
The relative frequency \(r_{0 - 2}=\frac{9}{38}\approx0.237\)

• For \(3 - 5\):

Count the numbers \(3,4,5\). The values are \(4,6,5,4,5,4\). So the frequency \(f_{3 - 5}=6\).
The relative frequency \(r_{3 - 5}=\frac{6}{38}\approx0.158\)

• For \(6 - 8\):

Count the numbers \(6,7,8\). The values are \(9,6,8,6,8,8,7,7,8,7\). So the frequency \(f_{6 - 8}=10\).
The relative frequency \(r_{6 - 8}=\frac{10}{38}\approx0.263\)

• For \(9 - 11\):

Count the numbers \(9,10,11\). The values are \(11,9,10,9,9\). So the frequency \(f_{9 - 11}=5\).
The relative frequency \(r_{9 - 11}=\frac{5}{38}\approx0.132\)

• For \(12 - 14\):

Count the numbers \(12,13,14\). The values are \(15,13,14,12,13,14,14\). So the frequency \(f_{12 - 14}=7\).
The relative frequency \(r_{12 - 14}=\frac{7}{38}\approx0.184\)

• For \(15 - 17\):

Count the numbers \(15,16,17\). The values are \(15,16,16\). So the frequency \(f_{15 - 17}=3\).
The relative frequency \(r_{15 - 17}=\frac{3}{38}\approx0.079\)

Answer:

Hours	Frequency	Relative Frequency
\(3 - 5\)	\(6\)	\(\frac{6}{38}\approx0.158\)
\(6 - 8\)	\(10\)	\(\frac{10}{38}\approx0.263\)
\(9 - 11\)	\(5\)	\(\frac{5}{38}\approx0.132\)
\(12 - 14\)	\(7\)	\(\frac{7}{38}\approx0.184\)
\(15 - 17\)	\(3\)	\(\frac{3}{38}\approx0.079\)