Question

HELP ASAP MY MOM SUPER MAD AT ME ASAP ASAP ASAP ASAP

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.

11, 18, 35, 39, 45, 45, 46, 47, 49, 49, 50, 50, 50, 50, 56, 57, 58, 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 center should the charity use to accurately represent the data? Explain your answer.

The median of 45.2 is the most accurate to use to show that they need more money.
The median of 49 is the most accurate to use, since the data is skewed.
The mean of 49 is the most accurate to use to show that they have plenty of money.
The mean of 45.2 is the most accurate to use, since the data is skewed.

Answer 1

The most appropriate measure of center for this data would be the median of 49.

The reason for this is that the data is skewed, with a cluster of higher donations between 45 and 50, and only a few donations in the lower range. The mean can be affected by outliers, and in this case, the presence of the two donations of 11 and 18 can skew the mean downwards. Therefore, the median, which is the middle value of the data set when arranged in order, is a more appropriate measure of center for this skewed distribution.

In this case, the median of 49 represents the middle value of the data set and is not influenced by the extreme values at either end of the distribution. Therefore, the charity can use the median donation amount of 49 dollars to accurately represent the typical donations received.