Number of goals scored in one season at Whitmore College soccer games follows:

Question

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 has outliers
MAD; the data distribution has outliers

IQR; the data distribution is symmetrical
IQR; the data distribution is symmetrical

MAD; the data distribution is symmetrical
MAD; the data distribution is symmetrical

IQR; the data distribution is skewed

Answer 1

To analyze the given dataset of goals scored at Whitmore College soccer games:

The data set is: 0, 0, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4

1. Identifying Outliers and Distribution:

   • The data does not seem to have significant outliers. The majority of scores are clustered around 2 and 3.
   • The distribution appears somewhat skewed, as there are more low scores (0's and 2's) than high scores.

2. Choosing the Measure of Variability:

   • IQR (Interquartile Range) is more suitable for describing the spread of data with outliers and non-symmetrical distributions, as it measures the range within which the central 50% of data points fall.
   • MAD (Mean Absolute Deviation) is less affected by extreme values but is more appropriate for symmetrical distributions.

Based on the data being somewhat skewed, the IQR would accurately reflect the spread of the dataset.

Thus, the best response is:

IQR; the data distribution is skewed.