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 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 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 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
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 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 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 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
Answers
GPT-4o mini
To determine whether the mean or median best represents the data set, we first need to calculate both values based on the goals scored in each of the 9 games.
The goals scored in each game are: 6, 1, 1, 0, 3, 1, 0, 3, 8.
**Step 1: Calculate the Mean**
To calculate the mean:
1. Sum the total goals scored:
\(6 + 1 + 1 + 0 + 3 + 1 + 0 + 3 + 8 = 23\)
2. Divide the sum by the number of games (9):
\[
\text{Mean} = \frac{23}{9} \approx 2.56
\]
**Step 2: Calculate the Median**
To find the median, we first need to order the goals scored:
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 number in the ordered list:
- The 5th value is **1**.
**Summary:**
- Mean: approximately **2.56**
- Median: **1**
**Step 3: Determine the Best Measure of Center**
The data set is somewhat right-skewed due to the higher number of goals in some games (e.g., 8 in one game). When data is skewed, the median can often be a better measure of central tendency because it is less affected by extreme values.
Therefore, the median value of 1 is the best measure of center that describes the shape of the data set. Thus, the correct response is:
**The median value of 1 is the best measure of center that describes the shape of the data set.**
The goals scored in each game are: 6, 1, 1, 0, 3, 1, 0, 3, 8.
**Step 1: Calculate the Mean**
To calculate the mean:
1. Sum the total goals scored:
\(6 + 1 + 1 + 0 + 3 + 1 + 0 + 3 + 8 = 23\)
2. Divide the sum by the number of games (9):
\[
\text{Mean} = \frac{23}{9} \approx 2.56
\]
**Step 2: Calculate the Median**
To find the median, we first need to order the goals scored:
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 number in the ordered list:
- The 5th value is **1**.
**Summary:**
- Mean: approximately **2.56**
- Median: **1**
**Step 3: Determine the Best Measure of Center**
The data set is somewhat right-skewed due to the higher number of goals in some games (e.g., 8 in one game). When data is skewed, the median can often be a better measure of central tendency because it is less affected by extreme values.
Therefore, the median value of 1 is the best measure of center that describes the shape of the data set. Thus, the correct response is:
**The median value of 1 is the best measure of center that describes the shape of the data set.**