Customers waiting at Ellerton Bank have been complaining about the amount of time they must wait in line. Managers at the bank, beginning to investigate the problem, have recorded sample waiting times for 19 customers at the bank. Here are the 19 waiting times (in minutes).2, 3, 4, 5, 5, 5, 6, 6, 9, 10, 11, 12, 15, 15, 20, 21, 28, 31, 37Send data to calculator86420Frequency862210816243240waiting time (in minutes)(a) Which measures of central tendency do not exist for this data set? Choose all that apply.MeanMedianModeNone of these measures(b) Suppose that the measurement 37 (the largest measurement in the data set) were replaced by 59. Which measures of central tendency would be affected by the change? Choose all that apply.MeanMedianModeNone of these measures(c) Suppose that, starting with the original data set, the largest measurement were removed. Which measures of central tendency would be changed from those of the original data set? Choose all that apply.MeanMedianModeNone of these measures(d) Which of the following best describes the distribution of the original data? Choose only one.
Question
Customers waiting at Ellerton Bank have been complaining about the amount of time they must wait in line. Managers at the bank, beginning to investigate the problem, have recorded sample waiting times for 19 customers at the bank. Here are the 19 waiting times (in minutes).2, 3, 4, 5, 5, 5, 6, 6, 9, 10, 11, 12, 15, 15, 20, 21, 28, 31, 37Send data to calculator86420Frequency862210816243240waiting time (in minutes)(a) Which measures of central tendency do not exist for this data set? Choose all that apply.MeanMedianModeNone of these measures(b) Suppose that the measurement 37 (the largest measurement in the data set) were replaced by 59. Which measures of central tendency would be affected by the change? Choose all that apply.MeanMedianModeNone of these measures(c) Suppose that, starting with the original data set, the largest measurement were removed. Which measures of central tendency would be changed from those of the original data set? Choose all that apply.MeanMedianModeNone of these measures(d) Which of the following best describes the distribution of the original data? Choose only one.
Solution
(a) All measures of central tendency exist for this data set. The mean, median, and mode can all be calculated from the given data.
(b) If the largest measurement in the data set (37) were replaced by 59, both the mean and median would be affected. The mean would increase because it is the average of all the data points, and replacing a lower number with a higher one would raise the average. The median would also increase because it is the middle value when the data points are arranged in numerical order, and replacing the largest number with an even larger one could shift the middle value. The mode would not be affected because it is the number that appears most frequently in the data set, and changing one number does not affect the frequency of the others.
(c) If the largest measurement were removed from the original data set, both the mean and median would be affected for the same reasons as in part (b). The mode would not be affected because it is based on frequency, not the actual values of the data points.
(d) Without a visual representation of the data, it's difficult to definitively describe the distribution. However, given the data points, it seems that the distribution of the original data is positively skewed. This is because the data has a long tail on the right (higher values), indicating that there are a few customers who wait significantly longer than most others.
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