Which measures of center will change when a value is added to this dataset?
Original dataset: (12,28,14,26,16,24,18,26,18,14,12,14)
New dataset with the value 14 inserted: (14,18,26,18,24,16,26,14,28,12,14,12,14)
Option #1: The mean and median will change.
Option #2: The mean and mode will change.
Option #3: The mode and median will change.
(1 point)
Option #
is the correct answer.
Which measures of center will change when a value is added to this dataset?
Original dataset: (12,28,14,26,16,24,18,26,18,14,12,14)
New dataset with the value 14 inserted: (14,18,26,18,24,16,26,14,28,12,14,12,14)
Option #1: The mean and median will change.
Option #2: The mean and mode will change.
Option #3: The mode and median will change.
(1 point)
Option #
is the correct answer.
Option #1: The mean and median will change.
Option #1: The mean and median will change.
To determine which measures of center will change when a value is added to a dataset, we need to calculate the mean, median, and mode of both the original and new datasets.
Original dataset: (12, 28, 14, 26, 16, 24, 18, 26, 18, 14, 12, 14)
1. Mean: The mean is calculated by summing all the values in the dataset and dividing by the total number of values. The mean of the original dataset is (12 + 28 + 14 + 26 + 16 + 24 + 18 + 26 + 18 + 14 + 12 + 14) / 12 = 214 / 12 = 17.83
2. Median: The median is the middle value of a sorted dataset. If there is an even number of values, the average of the two middle values is taken. Let's sort the original dataset: 12, 12, 14, 14, 14, 16, 18, 18, 24, 26, 26, 28. The median of the original dataset is (14 + 16) / 2 = 15.
3. Mode: The mode is the value(s) that appear(s) most frequently in the dataset. In the original dataset, the mode is 14 since it appears three times.
New dataset with value 14 inserted: (14, 18, 26, 18, 24, 16, 26, 14, 28, 12, 14, 12, 14)
1. Mean: The mean of the new dataset is (14 + 18 + 26 + 18 + 24 + 16 + 26 + 14 + 28 + 12 + 14 + 12 + 14) / 13 = 232 / 13 = 17.85
2. Median: Let's sort the new dataset: 12, 12, 14, 14, 14, 14, 16, 18, 18, 24, 26, 26, 28. The median of the new dataset is 14, which remains unchanged from the original dataset.
3. Mode: The mode of the new dataset is 14 since it appears four times.
Comparing the measures of center between the original and new datasets, we can conclude that the mean changes, but the median and mode (if there is one) remain the same. Therefore, the correct answer is Option #1: The mean and median will change.