To determine the best measure of center for the given dataset {0.06, 1, 1, 2, 3, 4, 4, 5, 6, 7, 8, 9, 9}, we can analyze the options: mode, mean, and median.
-
Mean: The mean is calculated by summing all the values and dividing by the number of values. \[ \text{Mean} = \frac{0.06 + 1 + 1 + 2 + 3 + 4 + 4 + 5 + 6 + 7 + 8 + 9 + 9}{13} = \frac{60.06}{13} \approx 4.63 \]
-
Median: The median is the middle value of the dataset when organized in ascending order. With 13 values (an odd number), the median is the 7th value.
- The ordered dataset is {0.06, 1, 1, 2, 3, 4, 4, 5, 6, 7, 8, 9, 9}.
- The 7th value is 4.
-
Mode: The mode is the value that appears most frequently. In this dataset, the modes are 1, 4, and 9 (each appears twice).
When considering the best measure of center, the median is often a better measure for skewed distributions or when there are outliers, as it is less affected by extreme values than the mean. In this dataset, the presence of the very small number (0.06) can skew the mean significantly.
Given that the median (4) and mode (1, 4, 9) reflect more typical values in the dataset, and considering the potential skewness caused by the low outlier, the median is indeed the best measure of center for this dataset.
Therefore, the best measure of center for the dataset is median.