To describe the center of the data, we can use either the mean or the median.
To describe the variation of the data, we can use either the range or the interquartile range (IQR).
Looking at the dot plot, it seems that the data is somewhat skewed to the right, with a few high-priced outliers. In this case, the median and the IQR may be more appropriate measures of the center and variation, respectively, as they are less sensitive to outliers.
To find the median and IQR:
Arrange the data in order from smallest to largest.
Find the median, which is the middle value. If there are an even number of values, take the average of the two middle values.
Find the first quartile, which is the median of the lower half of the data.
Find the third quartile, which is the median of the upper half of the data.
Calculate the IQR as the difference between the third quartile and the first quartile.
Here are the steps applied to the dot plot:
We can see that the smallest value is about 20 and the largest value is about 120, giving a range of 100 dollars.
The median is approximately 60 dollars, as it is the middle value between the 11th and 12th data points when the data is arranged in order.
The first quartile is approximately 40 dollars, as it isthe median of the lower half of the data points, which are found below the median.
The third quartile is approximately 80 dollars, as it is the median of the upper half of the data points, which are found above the median.
The IQR can be calculated as the difference between the third quartile and the first quartile, which is approximately 40 dollars.
Therefore, the most appropriate measures to describe the center and the variation for this data set are the median and the interquartile range (IQR), respectively. The median is approximately 60 dollars, and the IQR is approximately 40 dollars.