The following represents the number of hours per week 6 students spent playing video games: 5, 10, 8, 12, 4, and 7.

Question

If a new student joins the group and reports playing 20 hours per week, how will this affect the mean number of hours spent playing video games?

Answer 1

To find the effect of the new student's hours on the mean number of hours spent playing video games, we first need to calculate the current mean for the 6 students.

1. First, calculate the sum of the hours for the 6 students: \[ 5 + 10 + 8 + 12 + 4 + 7 = 46 \]

2. Then, calculate the current mean for these 6 students: \[ \text{Mean} = \frac{\text{Total hours}}{\text{Number of students}} = \frac{46}{6} \approx 7.67 \]

Next, we include the new student's hours (20 hours) and calculate the new mean.

3. Now, the new total sum of hours with the new student included is: \[ 46 + 20 = 66 \]

4. The new number of students is: \[ 6 + 1 = 7 \]

5. Now calculate the new mean: \[ \text{New Mean} = \frac{\text{New Total hours}}{\text{New Number of students}} = \frac{66}{7} \approx 9.43 \]

To summarize, the current mean is approximately 7.67 hours per week, and after the new student joins, the mean increases to approximately 9.43 hours per week. The inclusion of the new student significantly raises the overall mean.