Final answer:
The measures of the data set are: a mean of 52, a median of 65.2, a mode of 11.2, and a range of 90. The mean is influenced most by extreme values, particularly in skewed distributions.
Step-by-step explanation:
The measures for the data set 11.2, 101.2, 65.2, 71.2, 11.2 are:
- Mean: To find the mean, add all the numbers together and divide by the number of data points: (11.2 + 101.2 + 65.2 + 71.2 + 11.2) / 5 = 260 / 5 = 52.
- Median: The median is the middle number when the data is ordered from least to greatest. With our data set ordered as 11.2, 11.2, 65.2, 71.2, 101.2, the median is 65.2.
- Mode: The mode is the number that appears most frequently in the data set, which is 11.2.
- Range: The range is the difference between the highest and lowest values. The range of this data set is 101.2 - 11.2 = 90.
In reference to the provided information, the mean tends to reflect skewing the most because it includes all values, so extreme values can have a substantial impact. In a symmetrical distribution, the mean, median, and mode are all close to one another, but in a skewed distribution, they can differ significantly. The mode would differ from the mean and median in a symmetrical distribution if there are multiple peaks or a uniform distribution.