Number of goals scored in one season at Whitmore College soccer games follows:
0, 0, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4
Which measure of variability—IQR or MAD— best describes the spread of the dataset?
(1 point)
Responses
MAD; the data distribution is symmetrical
MAD; the data distribution is symmetrical
IQR; the data distribution is skewed
IQR; the data distribution is skewed
MAD; the data distribution has outliers
MAD; the data distribution has outliers
IQR; the data distribution is symmetrical
IQR; the data distribution is symmetrical
IQR; the data distribution is skewed
Of the mean, median, and mode, which measure of center is most affected by outliers? Explain your reasoning including an example with at least 10 data points
The mean is the measure of center that is most affected by outliers. This is because the mean is calculated by taking the sum of all the data points and dividing by the total number of data points, so even one outlier can significantly affect the calculation of the mean.
For example, consider the following set of data with 10 data points:
10, 12, 14, 15, 16, 18, 20, 22, 24, 500
The median of this data set is 17, which is not significantly affected by the outlier value of 500. The mode is not applicable as there are no repeated values.
However, the mean of this data set is calculated as:
(10 + 12 + 14 + 15 + 16 + 18 + 20 + 22 + 24 + 500) ÷ 10 = 61.9
As we can see, the presence of the outlier value of 500 has significantly skewed the value of the mean.
The correct answer is:
MAD; the data distribution has outliers
The dataset provided does not follow a symmetrical distribution, as there are several values that occur more frequently (2 and 3) compared to others (0 and 4). The IQR (Interquartile Range) is not an appropriate measure of variability in this case because it assumes a symmetrical distribution. MAD (Mean Absolute Deviation) is a better measure of variability when there are outliers present in the dataset.