What is the median of the following set of data values?
214, 322, 343, 432, 546, 567, 898, 5675.
Answer (2)
Sort the data set: 214, 322, 343, 432, 546, 567, 898, 5675.
Identify the two middle values: 432 and 546.
Calculate the average of the two middle values: 2 432 + 546 = 2 978 = 489 .
The median is 489 .
Explanation
Understanding the Problem We are given a set of 8 data values: 214, 322, 343, 432, 546, 567, 898, 5675. Our goal is to find the median of this data set. The median is the middle value when the data is sorted 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: 214, 322, 343, 432, 546, 567, 898, 5675.
Identifying the Middle Values Since there are 8 data values (an even number), the median is the average of the two middle values, which are the 4th and 5th values in the sorted data set. The 4th value is 432 and the 5th value is 546.
Calculating the Median Now, we calculate the average of 432 and 546. The average is calculated as follows:
2 432 + 546 = 2 978 = 489
So, the median is 489.
Final Answer Therefore, the median of the given data set is 489 .
Examples
The median is a useful measure in real-world scenarios, especially when dealing with data that might contain outliers. For example, when analyzing income data for a neighborhood, the median income gives a better sense of the 'typical' income than the average income, because very high incomes can skew the average. If the incomes in a neighborhood are: $25,000, $30,000, $35,000, $40,000, $45,000, $50,000, $60,000, and $1,000,000, the median income would be $42,500, while the average income would be significantly higher due to the one very high income. This makes the median a more robust measure of central tendency in many situations.
The median of the data set 214, 322, 343, 432, 546, 567, 898, 5675 is calculated as 489. This is done by sorting the data and finding the average of the two middle values, which are 432 and 546. Thus, the final median is 489.
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