Question

A class tracked the number of hours each student plays video games in a week. Answer the questions below. Based on the data in the line plot, calculate and show work for questions a-e. a) Find the mean. (3 points) b) Find the median (3 points) c) Find the mode. (2 points) d) Find the range. (2 points) e) What percentage of the students play video games for more than 4 hours (round to the nearest tenth)? (4 points)

Answer 1

`a.Mean=4.33hrs\\b.Median=3.5hrs\\c.Mode=3hrs\\d.44.44\%`

Explanation:

Let the
`X` markings denote students per hour.

a. Mean is the 'average' hr per unit student and is obtained by dividing the total number of hour played by total students.

From our data:
`Total \ students=18` (summing the X's)

`Total \ hours=78` (summing the product of students by corresponding hrs)

Hence:

`\bar X=(1)/((total students)\sum hours \ played)\\=(1)/(18)* 78=4.33hrs`

The mean is 4.33hrs

b.Median is the middle value in a list of data points arranged in ascending order. So, we find the number of hours played by the middle student.

Since our data is even, our middle student is

`(1)/(2)(9^t^h+10^t^h) student \ hrs\\=(1)/(2)(3+4)\\=3.5hrs`

The median is 3.5hrs

c.Mode is the most occuring data point. In our case the number of hours played by most students.

-From our data, we can observed that 3hrs has the most number of players (4 students).

-Our mode is then 3hrs.

d.To find percentage of students playing more than 4hrs, we first sum those playing 5+ hrs :

`t>4_h_r_s=2+2+1+2+1=8`

we then divide this value by total students and multiply by 100%

`=(8)/(18)* 100\%\\=44.44\%`

Hence 44.44% play more than 4hrs.