There are 16 observations arranged in increasing order of their values in a data. The median will be the value of

To find the median of a set of 16 observations arranged in increasing order, you can use the following method:

1. Arrange the data in increasing order.
2. Identify the middle position(s) of the data set.

Since there are 16 observations, an even number, the median is the average of the values at the \(\left(\frac{n}{2}\right)^{th}\) and \(\left(\frac{n}{2} + 1\right)^{th}\) positions.

For \(n = 16\):
- The \(\left(\frac{16}{2}\right)^{th}\) position is the 8th position.
- The \(\left(\frac{16}{2} + 1\right)^{th}\) position is the 9th position.

Therefore, the median is the average of the 8th and 9th values.

Mathematically, if the 8th value is \(x_8\) and the 9th value is \(x_9\), the median \(M\) is given by:
\[ M = \frac{x_8 + x_9}{2} \]

Do you want details or have any questions?

Here are 5 numbered questions for you to ask:

1. How do you find the median of an odd number of observations?
2. What is the difference between the mean and the median?
3. How do you calculate the mode of a data set?
4. Can you explain how to find the quartiles of a data set?
5. What is the impact of outliers on the median?

**Tip:** When dealing with an even number of observations, always remember that the median is the average of the two middle numbers.

Learn how to find the median of a set of 16 observations arranged in increasing order. Understand the method to determine the median for an even number of observations. Suitable for students in Grades 9-12.

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