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): 1,3,4,5,5,5,6,7,9,11,12,12,13,14,17,21,26,29,38. send data to calculator. (a) for these data, which measures of central tendency take more than one value? choose all that apply. mean median mode none of these measures. (b) suppose that the measurement 38 (the largest measurement in the data set) were replaced by 61. which measures of central tendency would be affected by the change? choose all that apply. mean median mode none of these measures. (c) suppose that, starting with the original data set, the smallest measurement were removed. which measures of central tendency would be changed from those of the original data set? choose all that apply. mean median mode none of these measures. (d) which of the following best describes the distribution of the original data? choose only. positively skewed negatively skewed

Explanation:

Step1: Recall properties of central - tendency measures

The mean is the sum of all data values divided by the number of data values. The median is the middle - value when the data is arranged in ascending or descending order. The mode is the most frequently occurring value.

Step2: Analyze effect of changing a single value

(a) If we change the largest value in the data - set, the mean will be affected because the sum of the data values changes. The median may or may not be affected depending on the position of the largest value in the ordered data - set. The mode may not be affected if the largest value is not the mode. So the mean is the measure that takes more than one value and is affected.
(b) If we replace 38 (the largest value) with 61, the mean will change because the sum of the data values changes. The median may or may not change (if the number of data points is odd and the largest value is not the middle - value, the median will remain the same; if the number of data points is even, the change in the largest value may or may not affect the median calculation). The mode will not be affected if 38 and 61 are not the mode. So the mean is the measure of central tendency that would be affected.
(c) If we remove the smallest value, the mean will change as the sum and the number of data points change. The median may or may not change depending on the number of data points. The mode may not change if the smallest value is not the mode. So the mean is the measure of central tendency that would be changed.
(d) To determine the skewness of the data, we can consider the relationship between the mean, median, and mode. If the mean > median > mode, the data is positively skewed. Looking at the frequency distribution, we can see that the tail of the distribution is on the right - hand side (towards the larger values). So the data is positively skewed.

Answer:

(a) Mean
(b) Mean
(c) Mean
(d) Positively skewed