Question

ush financial is examining the use of its midtown atm machine. the numbers of transactions made per day at this atm during the past 20 days are as follows. 52, 57, 63, 63, 66, 69, 71, 73, 73, 74, 75, 77, 77, 79, 81, 84, 86, 87, 91, 97
(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 97 (the largest measurement in the data set) were replaced by 152. 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 one.
negatively skewed
positively skewed
roughly symmetrical

Explanation:

Step1: Recall definitions

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

Step2: Analyze part (a)

Mean and median are unique for a given data - set. Mode can have more than one value if multiple values have the same highest frequency. Here, if multiple values occur with the highest frequency, mode can take more than one value.

Step3: Analyze part (b)

Mean is affected by extreme values. Changing 97 to 152 (an extreme value) will change the sum and thus the mean. Median is the middle value of ordered data. For 20 data points, the median is the average of 10th and 11th ordered values. Changing the largest value does not affect the middle values. Mode is the most frequent value, and changing the largest value does not affect the mode.

Step4: Analyze part (c)

Removing the smallest value will change the sum, so the mean will change. For 20 data points, the median is the average of 10th and 11th ordered values. Removing the smallest value may change the ordered list and thus the median. Mode is the most frequent value, and removing the smallest value may or may not change the mode depending on its frequency.

Step5: Analyze part (d)

In a positively - skewed distribution, the tail on the right (higher values) is longer. Looking at the data and the histogram, the higher values extend further out, so the distribution is positively skewed.

Answer:

(a) Mode
(b) Mean
(c) Mean, Median
(d) Positively skewed