A snowmobile company recorded the number of snowmobiles purchased by some counties in a state.
11 13 14 15 16 14 13 16 15 14
11 11 12 15 13 14 17 18 18 16
Which of the following is the best measure of center for this data?
The best measure of center for this data would be the median, as it would not be affected by extreme values or outliers.
11 11 11 12 13 13 13 14 14 14 :::: 14 15 15 15 16 16 16 17 18 18
14
The median in this dataset is 14, as it is the middle value when the numbers are arranged in numerical order.
To determine the best measure of center for the data provided, you would typically consider using either the mean or the median.
To find the mean:
1. Add up all the numbers in the dataset.
2. Divide the sum by the total number of data points.
For example, to find the mean for the data given:
11 + 13 + 14 + 15 + 16 + 14 + 13 + 16 + 15 + 14 + 11 + 11 + 12 + 15 + 13 + 14 + 17 + 18 + 18 + 16 = sum of the data points
Divide the sum by the total number of data points (20 in this case).
To find the median:
1. Arrange the data points in ascending order.
2. If the number of data points is odd, the median is the middle value.
3. If the number of data points is even, the median is the average of the two middle values.
For example, to find the median for the data given:
Arrange the data points in ascending order: 11, 11, 12, 13, 13, 14, 14, 14, 15, 15, 16, 16, 17, 18, 18
Since the number of data points is even (15 in this case), the median would be the average of the two middle values: (14 + 15) / 2 = 14.5.
Comparing the mean and median, the best measure of center depends on the specific characteristics of the dataset and the purpose of the analysis. The mean is affected by outliers, as it takes into account the value of each data point. The median, on the other hand, is less sensitive to outliers, as it focuses on the central values. If the dataset contains extreme values or if the distribution is skewed, the median might be a more appropriate measure of center. Otherwise, the mean can provide a more accurate representation of the overall average.