The dot plot below shows the number of hours that several sixth graders spent inside the school building in a day. Each X represents one student.
A dot plot showing hours from 0 to 8 in the increments of 1 has one X at 0, 2 X's at 7 and seven X's at 8.
Which of the following statements is true regarding this data? Select all that apply.
A.
The median better represents these data than the mean.
B.
The mean is affected by the one student who was absent from school.
C.
The distribution is skewed since most students were in the school building for 7 or 8 hours.
A. The median better represents these data than the mean.
C. The distribution is skewed since most students were in the school building for 7 or 8 hours.
A. The median better represents these data than the mean. (True)
C. The distribution is skewed since most students were in the school building for 7 or 8 hours. (True)
To answer this question, it is helpful to understand the concepts of median, mean, and skewed distributions. Let's go step by step.
First, let's define the terms:
- Median: The median is the middle value in a set of data when the data is arranged in ascending or descending order. It is a measure of central tendency that is not affected by extreme values.
- Mean: The mean is the average of a set of data, calculated by adding up all the values and dividing by the total number of values. It is also a measure of central tendency, but it can be influenced by extreme values.
- Skewed distribution: A distribution is considered skewed when it is not symmetrical. In a positively skewed distribution, the tail of the graph extends towards the higher values.
Now, let's analyze the statements:
A. "The median better represents these data than the mean":
In this case, the median would be a more appropriate measure of central tendency because extreme values, such as the 0 and the 8 hours, could heavily influence the mean. Since the data is skewed towards the higher values (7 and 8), the median would be less affected by these extreme values and provide a more representative measure.
B. "The mean is affected by the one student who was absent from school":
Given that the dot plot provided has only one X at 0, it implies that one student spent 0 hours in the school building. Since the mean takes into account all values, including the 0, it would be affected by this absence.
C. "The distribution is skewed since most students were in the school building for 7 or 8 hours":
From the given data, we can observe that there are more X's at 8 than at any other value, followed by 2 X's at 7. This concentration of values towards the higher end indicates a positively skewed distribution.
Therefore, the correct statements based on the given dot plot are:
A. The median better represents these data than the mean.
B. The mean is affected by the one student who was absent from school.
C. The distribution is skewed since most students were in the school building for 7 or 8 hours.
Remember, to analyze data accurately, it is always recommended to consider multiple measures of central tendency and evaluate the distribution of the data in order to make reliable conclusions.