Question

usm financial is examining the use of its midtown atm machine. the numbers of transactions made in a day at this atm for the past 20 days are as follows. 52, 59, 61, 62, 66, 66, 72, 72, 72, 73, 75, 76, 77, 78, 81, 83, 87, 89, 91, 97 send data to calculator answer the questions below. (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 52 (the smallest measurement in the data set) were replaced by 9. 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

Explanation:

Step1: Recall definitions

Mean is the sum of all data - points divided by the number of data - points. Median is the middle - value when data is ordered. Mode is the most frequently occurring value.

Step2: Answer part (a)

The mode can take more than one value if there are multiple values with the highest frequency. In a non - symmetric distribution, it's possible for the mode to have multiple values. Mean and median are single values for a given data set.

Answer:

for (a): Mode

Step3: Answer part (b)

The mean is calculated as $\frac{\sum_{i = 1}^{n}x_{i}}{n}$. Changing the value of 52 to 9 will change the sum $\sum_{i = 1}^{n}x_{i}$, so the mean will be affected. The median is the average of the 10th and 11th ordered values. Changing the smallest value does not affect the middle values (since the number of data points is 20). The mode is the most frequently occurring value, and changing the smallest value does not affect the mode.