The table below shows how many minutes Mary spent exercising each day for the last two weeks.
Mary's Time Spent Exercising
Sun Mon Tue Wed Thu Fri Sat
Week 1 0 min 45 min 45 min 40 min 50 min 35 min 0 min
Week 2 0 min 45 min 50 min 45 min 40 min 50 min 35 min
Which of the following best explains why the mean is NOT an appropriate indicator of how much time Mary spends exercising on a typical day?
A.
There is more than one mean.
B.
The mean is not an integer value.
C.
The mean is skewed by the days Mary did not exercise.
D.
The set of data points is too small
C. The mean is skewed by the days Mary did not exercise.
C. The mean is skewed by the days Mary did not exercise.
Explanation: The mean is calculated by summing up all the data points and dividing by the total number of data points. In this case, the days where Mary did not exercise (0 minutes) will have a significant impact on the mean since they are included in the calculation. This skews the mean, making it higher than what Mary typically spends exercising on a typical day.
The best way to determine why the mean is not an appropriate indicator in this case is to analyze the given data. The mean is calculated by adding up all the values and then dividing by the total number of values.
Looking at the table, we can see that Mary's time spent exercising varied from day to day. In Week 1, she did not exercise on Sunday and Saturday, while in Week 2, she did not exercise on Sunday. On the other days, her exercise time ranged from 35 to 50 minutes.
Option A, "There is more than one mean," is not applicable to this question as there is only one mean calculated for a given set of data.
Option B, "The mean is not an integer value," is not a valid reason since the mean does not have to be an integer. It can be a decimal value.
Option D, "The set of data points is too small," is also not a plausible explanation. While a larger data set may provide more accuracy, the size of this data set is sufficient to calculate a mean.
The correct answer is C, "The mean is skewed by the days Mary did not exercise." The mean is influenced by all the data points, including the days Mary did not exercise. In this case, since Mary did not exercise on certain days, these zero values will reduce the overall mean, leading to a potentially misleading representation of her typical exercise time.
To better analyze Mary's typical exercise time, other measures such as the median or mode may be more appropriate. The median represents the middle value when the data is sorted in order, while the mode represents the most frequently occurring value. These measures can provide a more accurate representation of Mary's typical exercise time, disregarding the days she did not exercise.