What is the median of the following data: 10, 12, 3, 4, 5, 8, 12, 15, 5, 6

What is the median of the following data: 10, 12, 3, 4, 5, 8, 12, 15, 5, 6?

The correct answer and explanation is:

Correct Answer: 7

Step-by-step Solution:

To find the median of a data set, follow these steps:

1. Arrange the numbers in ascending order: Given data:
   10, 12, 3, 4, 5, 8, 12, 15, 5, 6 Ordered:
   3, 4, 5, 5, 6, 8, 10, 12, 12, 15
2. Count the total number of values: There are 10 values.
3. Determine the position of the median:
   • If the number of data points (n) is odd, the median is the value at position (n + 1)/2.
   • If even, the median is the average of the two middle numbers, at positions n/2 and (n/2) + 1.
   Since we have 10 numbers (even), the median is the average of the 5th and 6th numbers.
   • 5th number = 6
   • 6th number = 8
   Median = (6 + 8) / 2 = 7

Explanation (300 words):

The median is a measure of central tendency that represents the middle value in a data set when the numbers are arranged in ascending or descending order. It is particularly useful in summarizing data because it is not affected by outliers or extremely high or low values. This makes it a better representation of the “typical” value in many cases than the mean.

In this case, the data set has 10 values:
10, 12, 3, 4, 5, 8, 12, 15, 5, 6

The first step in finding the median is sorting the data, which gives us:
3, 4, 5, 5, 6, 8, 10, 12, 12, 15

Since the total number of values is even (10), we don’t have a single middle number. Instead, the median is calculated as the average of the two central values — the 5th and 6th numbers in the sorted list. These are 6 and 8, respectively.

Taking the average of these two gives:
(6 + 8) ÷ 2 = 7

So, the median of this data set is 7.

Understanding the median helps in interpreting data distributions and spotting skewness. For example, in a salary distribution, the median gives a better picture of what most people earn compared to the mean, which might be inflated by a few high incomes.