What is the median number of cars sold this month?
Salesperson | Number of Cars Sold |
Frank | 25 |
Sara | 20 |
Randy | 15 |
Braheem | 22 |
Alice | 20 |
To find the median number of cars sold, we first need to gather all the individual sales data points from the provided table. We have the following data set for the five salespeople:
Our data set is \(S = \{25, 20, 15, 22, 20\}\). There are \(n = 5\) observations in total.
The median is defined as the middle value of a data set when it is arranged in numerical order. Since we have an odd number of observations (\(n = 5\)), the median will be the value located exactly at the center of the sorted list.
First, let's sort the sales numbers from least to greatest:
The sorted data set is \(S_{sorted} = \{15, 20, 20, 22, 25\}\).
To find the position of the median in an ordered list of \(n\) values, we use the formula \(\text{Position} = \frac{n + 1}{2}\).
For our data set where \(n = 5\):
\[\text{Position} = \frac{5 + 1}{2} = \frac{6}{2} = 3\]
The median is the value at the third position in our sorted list \(S_{sorted} = \{15, 20, 20, 22, 25\}\).
The value at the third position is \(20\). Therefore, the median number of cars sold is \(20\).
The median is a very useful statistical tool for summarizing data because it is not affected by extreme outliers. For instance, if you are looking at home prices in a neighborhood or salaries in a company, the median provides a more "typical" value than the mean (average), which can be skewed by one very high or low figure. Understanding how to find it helps you interpret everyday data reports accurately.