What is the median of the following scores: 19, 16, 2, 10, 15, 5, 17?
Understand the Problem
The question is asking for the median of a given set of scores, which involves sorting the numbers and identifying the middle value.
Answer
The median is the middle score or the average of the two middle scores in a sorted list.
Answer for screen readers
The median score is calculated as follows. If the sorted scores are, for example, [3, 5, 7], the median is $7$ since there are three scores (odd number). If the scores are [3, 5, 7, 9], then the median is $\frac{5 + 7}{2} = 6$.
Steps to Solve
- Sort the Data Set
Begin by listing the scores in numerical order from smallest to largest.
- Count the Number of Scores
Determine how many scores are present in your sorted list. This will help to figure out if the median is one middle score or the average of two middle scores.
- Identify the Median Position
If the number of scores ($n$) is odd, the median is the score at position $\frac{n+1}{2}$. If $n$ is even, the median is the average of the scores at positions $\frac{n}{2}$ and $\frac{n}{2} + 1$.
- Calculate the Median
For an odd number of scores, take the score in the middle. For an even number of scores, add the two middle scores together and divide by 2.
The median score is calculated as follows. If the sorted scores are, for example, [3, 5, 7], the median is $7$ since there are three scores (odd number). If the scores are [3, 5, 7, 9], then the median is $\frac{5 + 7}{2} = 6$.
More Information
The median is a useful measure of central tendency as it is less affected by outliers than the mean. This makes it a better measure when dealing with skewed distributions.
Tips
- Skipping the sorting step can lead to incorrect median calculation.
- Forgetting to check whether the number of scores is odd or even can cause confusion about which method to apply for finding the median.
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