The average of nine numbers is 50. The average of the first five numbers is 54 and that of the last three numbers is 52. Then the sixth number is 

The average of nine numbers is 50. The average of the first five numbers is 54 and that of the last three numbers is 52. Then the sixth number is

The sixth number is 24.

Let's denote the sum of the first five numbers as S1, the sum of the last three numbers as S2, and the sum of all nine numbers as S.

Given:

Average of nine numbers is 50, so

S = 9 * 50 = 450.

Average of the first five numbers is 54, so

S1 = 5 * 54 = 270.

Average of the last three numbers is 52, so

S2 = 3 * 52 = 156.

Now, we know that:

S = S1 + S2 + sixth number

Substituting the given values:

450 = 270 + 156 + sixth number

sixth number = 450 - 270 - 156

sixth number = 24

So, the sixth number is 24.

What is an Average? How to Find the Average?

An average, also known as a mean, is a measure of central tendency used to summarize a set of data points by representing a typical value within that set. It's calculated by adding up all the values in a data set and dividing the sum by the total number of values.

Here's a step-by-step guide to finding the average:

1. Add Up the Values: Start by adding together all the values in the data set.

2. Count the Number of Values: Determine how many values are in the data set. This will be the total number of items you added together in step 1.

3. Divide the Sum by the Count: Divide the sum from step 1 by the count from step 2. This will give you the average.

For example, let's say you have the following data set: 5, 8, 10, 12, 15.

1. Add up all the values: 5 + 8 + 10 + 12 + 15 = 50.
2. Count the number of values: There are 5 values in the data set.
3. Divide the sum by the count: 50 ÷ 5 = 10.

So, the average of this data set is 10.

Keep in mind that while the average gives you a single value to represent the central tendency of your data, it may not always provide a complete picture, especially if there are outliers or if the data is skewed. In such cases, it can be helpful to also consider other measures of central tendency such as the median or mode.