Questions: On each trial of an experiment, a participant is presented with a constant soft noise, which is interrupted at some unpredictable time by a slightly louder sound. The time it takes for the participant to react to the louder sound is recorded. The following list contains the reaction times (in milliseconds) for 25 trials of this experiment. 175, 205, 209, 218, 224, 236, 262, 262, 262, 266, 275, 305, 320, 333, 334, 340, 377, 398, 400, 405, 444, 475, 596, 661, 776 (a) Which measures of central tendency do not exist for this data set? Choose all that apply. - Mean - Median - Mode - All of these measures exist (b) Suppose that the measurement 175 (the smallest measurement in the data set) were replaced by 68. 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 largest 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) The relative values of the mean and median for the original data set are typical of data that have a significant skew to the right. What are the relative values of the mean and median for the original data set? Choose only one. - Mean is greater - Median is greater - Cannot be determined

On each trial of an experiment, a participant is presented with a constant soft noise, which is interrupted at some unpredictable time by a slightly louder sound. The time it takes for the participant to react to the louder sound is recorded. The following list contains the reaction times (in milliseconds) for 25 trials of this experiment. 175, 205, 209, 218, 224, 236, 262, 262, 262, 266, 275, 305, 320, 333, 334, 340, 377, 398, 400, 405, 444, 475, 596, 661, 776 (a) Which measures of central tendency do not exist for this data set? Choose all that apply. - Mean - Median - Mode - All of these measures exist (b) Suppose that the measurement 175 (the smallest measurement in the data set) were replaced by 68. 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 largest 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) The relative values of the mean and median for the original data set are typical of data that have a significant skew to the right. What are the relative values of the mean and median for the original data set? Choose only one. - Mean is greater - Median is greater - Cannot be determined
Transcript text: On each trial of an experiment, a participant is presented with a constant soft noise, which is interrupted at some unpredictable time by a slightly louder sound. The time it takes for the participant to react to the louder sound is recorded. The following list contains the reaction times (in milliseconds) for 25 trials of this experiment. \[ 175,205,209,218,224,236,262,262,262,266,275,305,320,333,334,340,377,398,400,405,444,475,596,661,776 \] (a) Which measures of central tendency do not exist for this data set? Choose all that apply. - Mean - Median - Mode - All of these measures exist (b) Suppose that the measurement 175 (the smallest measurement in the data set) were replaced by 68. 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 largest 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) The relative values of the mean and median for the original data set are typical of data that have a significant skew to the right. What are the relative values of the mean and median for the original data set? Choose only one. - Mean is greater - Median is greater - Cannot be determined
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Solution

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Solution Steps

Step 1: Identifying Existing Measures of Central Tendency

The mean, median, and mode all exist for this dataset. The mean is the average of all values. The median is the middle value when the data is ordered. The mode is the most frequent value. Since all these can be calculated for the given dataset, all these measures exist.

Step 2: Effect of Replacing the Smallest Value

If 175 is replaced by 68, the mean would be affected because the sum of the values would change, and the mean is calculated using the sum. The median would not be affected because the median is the middle value when the data is ordered. 68 would become the smallest value, but 175 is already the smallest, so replacing the smallest with a smaller number doesn't change the middle value. The mode (262) also would not be affected because 175 only appears once, and changing it to 68 doesn't affect the frequency of 262.

Step 3: Effect of Removing the Largest Value

If the largest measurement (776) is removed, the mean would change because the sum of the values and the number of values would both change. The median would also change because the number of data points changes from odd to even, and the median would now be the average of the 12th and 13th values once ordered. The mode would not change because removing the largest value does not affect the frequency of the other values.

Final Answer

(a) All of these measures exist. (b) Mean (c) Mean, Median (d) Mean is greater

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