To analyze the data from the dot plot:
The ages and their corresponding frequencies are:
- 12: 1 student
- 13: 2 students
- 14: 6 students
- 15: 2 students
- 16: 1 student
From this data, we can derive several insights to evaluate the given statements:
-
Distribution: The distribution is not symmetric; it is skewed to the right because 14 has the highest frequency and there are fewer students at the lower and higher ends (12 and 16, respectively). Therefore, Statement A (The distribution is symmetric) is false.
-
Maximum Age: The maximum age is 16, but using the maximum age to describe data can be misleading, especially in a skewed distribution. The maximum only provides one data point and does not account for the distribution of the other ages. Therefore, Statement B (The maximum age would best describe the ages of the students in the play) is false.
-
Mean and Median:
- To find the median, we should arrange the ages: 12, 13, 13, 14, 14, 14, 14, 14, 14, 15, 15, 16. There are a total of 12 students.
- The median is determined by the average of the 6th and 7th values: (14 + 14) / 2 = 14.
- To find the mean, we take the total of the ages: (12 + 13×2 + 14×6 + 15×2 + 16) / 12 = (12 + 26 + 84 + 30 + 16) / 12 = 168 / 12 = 14.
- Both the mean and the median are equal to 14. Therefore, Statement C (The mean and the median are the same) is true.
-
Mean and Median Representation: Given that the mean and median are both the same and reflect the central tendency, they are appropriate measures to represent the ages of the students. Therefore, Statement D (The mean and the median would best represent the ages of the students) is true.
In conclusion, the true statements regarding the data are:
- C. The mean and the median are the same.
- D. The mean and the median would best represent the ages of the students.
1 answer