Use the table to answer the question.

This table shows the number of goals scored in each of the 9 games.
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?(1 point)
Responses

The mean value of 1 is the best measure of center that describes the shape of the data set.
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 mean value of 2.6 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 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 1 is the best measure of center that describes the shape of the data set.

1 answer

To determine whether the mean or the median best describes the shape of the data set, we first need to calculate both the mean and the median of the number of goals scored.

Goals Scored:

  • Game 1: 6
  • Game 2: 1
  • Game 3: 1
  • Game 4: 0
  • Game 5: 3
  • Game 6: 1
  • Game 7: 0
  • Game 8: 3
  • Game 9: 8

Step 1: Calculate the mean.

Mean = (Sum of all goals scored) / (Number of games)

Sum = 6 + 1 + 1 + 0 + 3 + 1 + 0 + 3 + 8 = 23
Number of games = 9

Mean = 23 / 9 ≈ 2.56 (rounded to 2.6)

Step 2: Calculate the median.

To find the median, we need to arrange the data in ascending order: 0, 0, 1, 1, 1, 3, 3, 6, 8

Since there are 9 data points (an odd number), the median is the middle value, which is the 5th value in the ordered list.

Median = 1 (the 5th value in the sorted list)

Conclusion:

  • Mean = 2.6
  • Median = 1

Given that the data has several low values (especially a couple of zeros), it is skewed left. Therefore, the median is less affected by extreme values than the mean.

The correct response is: The median value of 1 is the best measure of center that describes the shape of the data set.