Question

The class tracked the hours each student played games per month. Answer the questions below.

Based on the data in the line plot, calculate the a-d. Explain (or show work) how you found each answer.

Find the mean:


Find the median:

Find the mode:

What percentage of students play video games for more than four hours per week (round to the nearest tenth)

Answer 1

a) The mean is about 4.3 hours

b) The median is 3.5 hours

c) The mode is 3 hours

d) The percentage of students play video games for more than four hours per week is about 44.4%

Explanation:

Let us revise some definitions

• The mean is the "average", where you add up all the numbers and then divide by the number of numbers
• The median is the "middle" value in the list of numbers arranged from small to large
• The mode is the most repeated number in the list of data

The data from the line plot is

Number of hour → 1 : 2 : 3 : 4 : 5 : 6 : 7 : 8 : 9

Number of Student → 2 : 3 : 4 : 1 : 2 : 2 : 1 : 2 : 1

Let us find the total number of students

The number of students = 2 + 3 + 4 + 1 + 2 + 2 + 1 + 2 + 1

The number of students = 18

Let us find the sum of the number of the hours by multiplying the number of the students times the number of the hours that they played

The sum = 1×2 + 2×3 + 3×4 + 4×1 + 5×2 + 6×2 + 7×1 + 8×2 + 9×1

The sum = 2 + 6 + 12 + 4 + 10 + 12 + 7 + 16 + 9

The sum = 78

The mean = sum ÷ number

The mean = 78 ÷ 18 = 4.33333

a) The mean is about 4.3 hours

The number of students is 18

To find the median, find the middle student

The number of students is even number, then the middle of them will be the 9th and the 10th (before them 8 students and after them 8 students), So let us find the number of hours of the 9th and 10th students and calculate the average of their hours

The 9th played for 3 hours and the 10th played for 4 hours

The median =
`(3+4)/(2)` = 3.5

b) The median is 3.5 hours

The mode is the must repeated number, so look for the hour with greatest number of students

From the line plot there are in 3 hours 4 students and it is the greatest number of students, so the mode is 3 hours

c) The mode is 3 hours

Let us count the number of students who played more than 4 hours

2 in 5 hrs, 2 in 6 hrs, 1 in 7 hrs, 2 in 8 hrs and 1 in 9 hrs

The number of students = 2 + 2 + 1 + 2 + 1 = 8

The percentage = (number of students who played more than 4 hours ÷ total number of students) × 100%

The percentage =
`(8)/(18)` × 100%

The percentage = 44.4444 %

d) The percentage of students play video games for more than four hours per week is about 44.4%