Question

A charity needs to report its typical donations received. The following is a list of the donations from one week. A histogram is provided to display the data.

5, 5, 6, 8, 10, 15, 18, 20, 20, 20, 20, 20, 20

A graph titled Donations to Charity in Dollars. The x-axis is labeled 1 to 5, 6 to 10, 11 to 15, and 16 to 20. The y-axis is labeled Frequency. There is a shaded bar up to 2 above 1 to 5, up to 3 above 6 to 10, up to 1 above 11 to 15, and up to 7 above 16 to 20.

Which measure of variability should the charity use to accurately represent the data? Explain your answer.

The range of 13 is the most accurate to use, since the data is skewed.
The IQR of 13 is the most accurate to use, since the data is skewed.
The range of 20 is the most accurate to use to show that they have plenty of money.
The IQR of 20 is the most accurate to use to show that they need more money.

Answer 1

The IQR of 13 is the most accurate measure of variability to use to represent the data. The range can give us an idea of the spread of the data, but since the data is skewed with a majority of donations at $20, the IQR will give us a better understanding of the central tendency of the donations. The IQR takes into account the middle 50% of the data, which is more relevant in this case. Additionally, the IQR is less sensitive to extreme values or outliers, which is useful when dealing with a skewed dataset.