Question

Question 4(Multiple Choice Worth 2 points)

(Appropriate Measures MC)

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.

10, 11, 35, 39, 40, 42, 42, 45, 49, 49, 51, 51, 52, 53, 53, 54, 56, 59

A graph titled Donations to Charity in Dollars. The x-axis is labeled 10 to 19, 20 to 29, 30 to 39, 40 to 49, and 50 to 59. The y-axis is labeled Frequency. There is a shaded bar up to 2 above 10 to 19, up to 2 above 30 to 39, up to 6 above 40 to 49, and up to 8 above 50 to 59. There is no shaded bar above 20 to 29.

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 49 is the most accurate to use to show that they need more money.
The range of 49 is the most accurate to use to show that they have plenty of money.
The IQR of 13 is the most accurate to use, since the data is skewed.

Answer 1

The IQR of 13 is the most accurate to use, since the data is skewed. The reason for this is that the data is not evenly distributed, as shown by the histogram with a large number of donations in the higher range. The IQR is a measure of variability that is less sensitive to outliers and skewed data than the range, which makes it a better choice for this type of data. Additionally, the IQR can provide information on the spread of the middle 50% of the data, which can be useful in understanding the typical donation range for the charity.