Question

HELP PLEASE I NEED HELP

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

Explanation:

The best measure of center for this data is the median, and its value is 49.

What is the median in statistics?

In statistics, the median is a measure of central tendency that represents the value separating the higher half of a dataset from the lower half.

To find the median of a dataset, the values must first be arranged in order of magnitude. If the dataset has an odd number of values, the median is the middle value. If the dataset has an even number of values, the median is the average of the two middle values.

To determine the best measure of center for this data, we need to consider the shape of the distribution. Looking at the histogram, we can see that the data is skewed to the right, with a long tail of higher values.

In this case, the median is the best measure of center, because it is not affected by the extreme values in the dataset. The median is the middle value of the dataset when it is arranged in order, and in this case, the middle value is between 49 and 50. Since there are an even number of data points, we take the average of the two middle values, which gives a median of 49.

We are given that;

The list of donation is as follows

11, 18, 35, 39, 45, 45, 46, 47, 49, 49, 50, 50, 50, 50, 56, 57, 58, 59

Now,

Mean is the middle term of the data

Here,

Middle term of data = 49

Therefore, the mean of the given list will be 49.

Therefore, the best measure of center for this data is the median, and its value is 49.