Question

Question 2 of 5

Participants in a survey were asked the number of hours of television they watch each week. The dot plot shows the distribution of
their responses.
0,2,2,2,3,4,4,5,5,6,6,7,7,7,8,10,10,12,14,15,15,16
Number of Hours
After the data was recorded in the dot plot, another response was found for a participant who watches 30 hours of television each
week. How will this additional data point affect the mean number of hours of television watched each week?
The mean number of hours will increase.
The effect on the mean number of hours cannot be determined.
The mean number of hours will decrease.
The mean number of hours will remain the same.

Answer 1

Answer:The mean number of hours will increase

Explanation:

Step 1: Calculate the sum of the existing data points:

0 + 2 + 2 + 2 + 3 + 4 + 4 + 5 + 5 + 6 + 6 + 7 + 7 + 7 + 8 + 10 + 10 + 12 + 14 + 15 + 15 + 16 = 190.

Step 2: Count the total number of data points (including the additional data point): 22 + 1 = 23.

Step 3: Add the value of the additional data point: 190 + 30 = 220.

Step 4: Calculate the new mean: 220 / 23 = 9.565.

Explanation:

The existing data points are summed up to get a total of 190 hours.

Including the additional data point, there are a total of 23 data points.

The value of the additional data point, 30, is added to the total sum of hours, resulting in a sum of 220.

The new sum (220) is divided by the total number of data points (23) to calculate the new mean, which is approximately 9.565.

Therefore, the mean number of hours of television watched each week will increase when the additional data point of 30 hours is included.

Answer 2

The additional data point of a participant watching 30 hours of television each week will affect the mean number of hours of television watched.

Explanation:

In this case, since the new data point of 30 is significantly larger than the rest of the data points, it will increase the overall average. Therefore, the correct answer is: "The mean number of hours will increase."