Find the median for $12,16,10,14,20,22,15,24$.
Answer (1)
Sort the data set in ascending order: 10 , 12 , 14 , 15 , 16 , 20 , 22 , 24 .
Identify the two middle values: 15 and 16.
Calculate the average of the two middle values: 2 15 + 16 = 15.5 .
The median of the data set is 15.5 .
Explanation
Understanding the Problem We are given the data set 12 , 16 , 10 , 14 , 20 , 22 , 15 , 24 and asked to find the median. The median is the middle value of a data set when the data is arranged in ascending order. If there is an even number of data points, the median is the average of the two middle values.
Sorting the Data First, we need to sort the data set in ascending order. The sorted data set is 10 , 12 , 14 , 15 , 16 , 20 , 22 , 24 .
Finding the Middle Values Next, we need to find the middle value(s). Since there are 8 data points, which is an even number, we need to find the two middle values. The two middle values are the 4th and 5th values in the sorted data set, which are 15 and 16.
Calculating the Median Finally, we calculate the average of the two middle values to find the median. The average of 15 and 16 is 2 15 + 16 = 2 31 = 15.5 .
Final Answer Therefore, the median of the data set is 15.5.
Examples
The median is a useful measure of central tendency that is less sensitive to outliers than the mean. For example, if you have a set of house prices in a neighborhood, the median house price will give you a better idea of the typical house price than the mean house price if there are a few very expensive houses that skew the mean. Understanding how to calculate the median helps in analyzing various data sets, from financial data to survey results, providing a more robust understanding of central tendencies.
