Final answer:
The shape of the distribution when using IQR cannot be determined; IQR only measures the spread of the middle 50% of the data and does not give information about the distribution's overall shape.
Step-by-step explanation:
The shape of the distribution when using the Interquartile Range (IQR) to measure spread cannot be determined. The IQR measures the spread of the middle 50% of the data, but it does not provide information about the overall shape of the data distribution.
Whether a distribution is symmetric, skewed left, or skewed right, the IQR only tells us about the variability within the central portion of the data. To understand more about the shape of the distribution, we need to look at a histogram or a box plot and consider other measures of skewness.
For example, if a distribution is skewed to the right, meaning it has a long tail to the right, the mean is typically greater than the median.
Conversely, if a distribution is skewed to the left, the mean is typically less than the median. In symmetric distributions, the mean and median are usually very close in value. However, none of these relationships can be inferred from the IQR alone.