To determine the correct statement about Group B compared to Group A, we need to look at both the mean and median of the two groups. Here is a detailed step-by-step solution:
Step 1: Calculate the Mean for Both Groups
The mean (average) is calculated by summing all the values in a group and then dividing by the number of values.
For Group A, the values are: 11, 21, 12, 18, 23
[tex]\[
\text{Mean of Group A} = \frac{11 + 21 + 12 + 18 + 23}{5} = \frac{85}{5} = 17
\][/tex]
For Group B, the values are: 15, 22, 18, 21, 14
[tex]\[
\text{Mean of Group B} = \frac{15 + 22 + 18 + 21 + 14}{5} = \frac{90}{5} = 18
\][/tex]
Step 2: Calculate the Median for Both Groups
The median is the middle value when the values are arranged in ascending order.
For Group A, the values in ascending order are: 11, 12, 18, 21, 23
[tex]\[
\text{Median of Group A} = 18 \quad \text{(the middle value)}
\][/tex]
For Group B, the values in ascending order are: 14, 15, 18, 21, 22
[tex]\[
\text{Median of Group B} = 18 \quad \text{(the middle value)}
\][/tex]
Step 3: Compare the Means and Medians
From the calculations:
- The mean of Group A is 17.
- The median of Group A is 18.
- The mean of Group B is 18.
- The median of Group B is 18.
Step 4: Determine the Correct Statement
We need to find the statement that matches these comparisons:
1. The mean of Group B is smaller than Group A, and the median is larger.
2. The mean of Group B is smaller than Group A, and the median is the same.
3. The mean of Group B is larger than Group A, and the median is larger.
4. The mean of Group B is larger than Group A, and the median is the same.
Given the results:
- The mean of Group B (18) is larger than the mean of Group A (17).
- The median of Group B (18) is the same as the median of Group A (18).
Therefore, the correct statement is:
4. The mean of Group B is larger than Group A, and the median is the same.
