Final answer:
The mean of the given data set is 12.25, the median is 15, and the mode is 5 and 18, indicating a bimodal distribution. The distribution seems to be somewhat right-skewed since the mean is pulled towards the higher values.
Step-by-step explanation:
To calculate the mean, median, and mode of the data values 5, 14, 18, 2, 16, 5, 18, 20, we first need to arrange the data in ascending order: 2, 5, 5, 14, 16, 18, 18, 20.
The mean (or average) is calculated by adding all the numbers together and dividing by the count of numbers. In this case, (2 + 5 + 5 + 14 + 16 + 18 + 18 + 20) / 8 = 98 / 8 = 12.25.
The median is the middle number in a sorted list. With an even number of values, it is the average of the two middle numbers. Here, the middle numbers are 14 and 16, so the median is (14 + 16) / 2 = 30 / 2 = 15.
The mode is the most frequently occurring number in a set of values. For this data set, the mode is 5 and 18, since they both occur twice. This makes the distribution bimodal.
When evaluating the shape of the distribution, we notice that the mean is less than the middle two numbers, but more than the median. This suggests the distribution might be slightly skewed to the right because the mean is higher than the median. However, we need to consider the other values to be sure about the skewness.
The typical relationship in a skewed distribution is that the mean is pulled towards the tail, and in this case, since the mean is less than some of the higher values but greater than the median, it supports the conclusion that the distribution is right-skewed. This is also supported by the fact that there are more frequent occurrences of higher values (18) among the higher end of the data.