Use the table to answer the question.
Game Goals Scored
1 6
2 1
3 1
4 0
5 3
6 1
7 0
8 3
9 8
What value, the mean or median, best describes the shape of the data set that contains the number of goals scored by the soccer team
Responses
The mean value of 1 is the best measure of center that describes the shape of the data set.
The mean value of 2.6 is the best measure of center that describes the shape of the data set.
The median value of 1 is the best measure of center that describes the shape of the data set.
The median value of 2.6 is the best measure of center that describes the shape of the data set.
The median value of 1 is the best measure of center that describes the shape of the data set.
A dump truck driver must haul 112 cubic yards of dirt to a construction site. The maximum load for the dump truck is 14 cubic yards. Which inequality represents the solution set that shows the number of loads, n, that the dump truck driver will haul?
Responses
A n ≤ 12n ≤ 12
B n ≥ 8n ≥ 8
C n ≥ 12n ≥ 12
D n ≤ 8
The correct answer is C. n ≥ 12.
To get to this solution, you can divide the total amount of dirt by the maximum load of the dump truck:
112 ÷ 14 = 8
So the driver will require 8 loads in total. However, the question is asking for an inequality that represents the possible number of loads the driver will haul. Since the driver cannot haul a fraction of a load, they will need to haul at least 8 loads (n ≥ 8). Additionally, since 8 loads may not be enough if the driver encounters any problems (such as spillage or uneven loading), the driver may need to haul more than 8 loads. Therefore, the solution set is n ≥ 8, or n ≥ 12 (since the next whole number greater than 8 that is a multiple of 14 is 12).
To find the measure of center that best describes the shape of the data set, we can compare the mean and median.
To calculate the mean, we add up all the goals scored and divide by the number of games:
(6 + 1 + 1 + 0 + 3 + 1 + 0 + 3 + 8) / 9 = 23 / 9 = 2.56 (rounded to two decimal places)
To find the median, we arrange the data set in ascending order:
0, 0, 1, 1, 1, 3, 3, 6, 8.
Since there are 9 values, the median is the middle value, which is 1.
Comparing the mean and median, we can conclude that the median value of 1 is the best measure of center that describes the shape of the data set in this case.