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.

10, 10, 10, 10, 15,15,15,19, 20, 20, 20, 25, 25, 25, 30, 30, 55, 55

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 8 above 10 to 19, up to 6 above 20 to 29, up to 2 above 30 to 39, and up to 2 above 50 to 59. There is no shaded bar above 40 to 49.

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

The median of 22.7 is the most accurate to use to show that they have plenty of money.
The mean of 20 is the most accurate to use to show that they need more money.
The median of 20 is the most accurate to use, since the data is skewed.
The mean of 22.7 is the most accurate to use, since the data is skewed.

Answer 1

Answer: C. The most accurate measure of center to represent the data in this case is the median of 20.

Step-by-step explanation: The median is the middle value in a dataset when the data is arranged in ascending or descending order. In this case, the donations are: 10, 10, 10, 10, 15, 15, 15, 19, 20, 20, 20, 25, 25, 25, 30, 30, 55, 55.

When we arrange these values in ascending order, we get: 10, 10, 10, 10, 15, 15, 15, 19, 20, 20, 20, 25, 25, 25, 30, 30, 55, 55.

The median is the value that separates the dataset into two equal halves. In this case, there are 18 values, so the middle value is the 9th value, which is 20.

The reason the median is the most accurate measure of center to use in this case is because the data is skewed. Skewness refers to the asymmetry in the distribution of data. In this case, the data is skewed to the right because there are a few large values (55) that pull the mean higher than the majority of the values.

Using the mean, which is calculated by summing all the values and dividing by the total number of values, would be influenced by these large values and may not accurately represent the typical donations received by the charity.