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.
The dot plot shows the number of hours that several sixth graders spent inside the school building in a day. Here are the statements and their corresponding answers:
A. The median better represents these data than the mean.
- This statement is true. In this case, the median is a more appropriate measure of central tendency because it is less affected by extreme values. The presence of two students at 7 hours and seven students at 8 hours makes the mean susceptible to being pulled towards higher values.
B. The mean is affected by the one student who was absent from school.
- This statement is false. The mean is not affected by the absence of a student since the dot plot only shows the number of hours for the students present. The mean would only be affected if the absence of one student changed the total number of students in the data set.
C. The distribution is skewed since most students were in the school building for 7 or 8 hours.
- This statement is false. The dot plot does not provide enough information to determine if the distribution is skewed. Skewness refers to the elongation of the distribution in one direction. In this case, we would need additional information such as the presence of outliers or the overall shape of the distribution to determine if it is skewed or not.
Therefore, the correct statement(s) are:
A. The median better represents these data than the mean.
To determine which statements are true regarding the given data, let's analyze each option:
A. The median better represents these data than the mean.
To find the median, we arrange the data in ascending order and identify the middle value. In this case, the data is as follows: 0, 7, 7, 8, 8, 8, 8, 8, 8, 8. There are 10 data points, so the middle value is the 5th one, which is the first 8. Since the median (8 hours) is representative of the value at the center of the data set, statement A is true.
B. The mean is affected by the one student who was absent from school.
To find the mean, we sum up all the data values and divide by the total number of values. In this case, there are 10 data points: 0, 7, 7, 8, 8, 8, 8, 8, 8, 8. Adding them up gives us 80. Dividing by 10 gives us a mean of 8. So, since the absence of a student with 0 hours does not affect the sum or average (mean) of the other values, statement B is false.
C. The distribution is skewed since most students were in the school building for 7 or 8 hours.
Skewness refers to the lack of symmetry in a distribution. In this case, if most students were in the school building for 7 or 8 hours, the distribution would be considered skewed. Therefore, statement C is true.
In summary, the true statements are:
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.