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 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
Explore the mystery of the sixth number in a sequence where the average of nine numbers is 50, with the initial five averaging 54 and the last three reaching 52.
by Maivizhi A
Updated Mar 06, 2024
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 stepbystep guide to finding the average:

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

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.

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.
 Add up all the values: 5 + 8 + 10 + 12 + 15 = 50.
 Count the number of values: There are 5 values in the data set.
 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.
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  FAQs
1. What is the concept of an average?
An average, or mean, is a statistical measure used to represent the central tendency of a set of data. It's calculated by adding up all values and dividing by the total count.
2. How do you find the average of a set of numbers?
To find the average, sum up all the numbers in the set and divide by the total count of numbers in the set.
3. What is the formula for finding the average?
The formula for finding the average is: Average = Sum of all values / Total count of values.
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