Question

a researcher gathered data on hours of video games played by school - aged children and young adults. she collected the following data:
1 8 8 4 2 15 7 6 12 6
13 9 14 6 15 1 17 13 7 9
12 3 5 3 11 15 10 8 7 3
2 12 12 7 2 12 17 0
(a) complete the frequency distribution for the data.
hours frequency relative frequency
0 - 2
3 - 5
6 - 8
9 - 11
12 - 14
15 - 17

Explanation:

Step1: Count the total number of data points

Count all the numbers in the given data set. There are \(40\) data points.

Step2: Calculate frequency for \(0 - 2\)

Numbers in the range \(0 - 2\): \(0,1,1,2,2,2,2\). Frequency \(f_{0 - 2}=7\). Relative frequency \(rf_{0 - 2}=\frac{7}{40}=0.175\)

Step3: Calculate frequency for \(3 - 5\)

Numbers in the range \(3 - 5\): \(3,3,3,4,5\). Frequency \(f_{3 - 5}=5\). Relative frequency \(rf_{3 - 5}=\frac{5}{40}=0.125\)

Step4: Calculate frequency for \(6 - 8\)

Numbers in the range \(6 - 8\): \(6,6,6,7,7,7,7,8,8,8\). Frequency \(f_{6 - 8}=10\). Relative frequency \(rf_{6 - 8}=\frac{10}{40}=0.25\)

Step5: Calculate frequency for \(9 - 11\)

Numbers in the range \(9 - 11\): \(9,9,10,11\). Frequency \(f_{9 - 11}=4\). Relative frequency \(rf_{9 - 11}=\frac{4}{40}=0.1\)

Step6: Calculate frequency for \(12 - 14\)

Numbers in the range \(12 - 14\): \(12,12,12,12,13,13,14\). Frequency \(f_{12 - 14}=7\). Relative frequency \(rf_{12 - 14}=\frac{7}{40}=0.175\)

Step7: Calculate frequency for \(15 - 17\)

Numbers in the range \(15 - 17\): \(15,15,15,17,17\). Frequency \(f_{15 - 17}=5\). Relative frequency \(rf_{15 - 17}=\frac{5}{40}=0.125\)

Answer:

Hours	Frequency	Relative Frequency
\(3 - 5\)	\(5\)	\(0.125\)
\(6 - 8\)	\(10\)	\(0.25\)
\(9 - 11\)	\(4\)	\(0.1\)
\(12 - 14\)	\(7\)	\(0.175\)
\(15 - 17\)	\(5\)	\(0.125\)