If the mean deviation about the mean of the numbers 1, 2, 3, …. n, where n is odd, is \(\frac{5(n + 1)}{n}\), then n is equal to ______.
Correct Answer: 21
Solution and Explanation
The correct answer is: 21
Mean
\(=\frac{\frac{n(n+1)}{2}}{n}=\frac{n+1}{2}\)
\(⇒((n-1)+(n-3)+(n-5)+...0=5)=5(n+1)\)
\(⇒(\frac{n+1}{4})(n-1)=5(n+1)\)
So, n = 21.
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Concepts Used:
Mean Deviation
A statistical measure that is used to calculate the average deviation from the mean value of the given data set is called the mean deviation.
The Formula for Mean Deviation:
The mean deviation for the given data set is calculated as:
Mean Deviation = [Σ |X – µ|]/N
Where,
- Σ represents the addition of values
- X represents each value in the data set
- µ represents the mean of the data set
- N represents the number of data values
Grouping of data is very much possible in two ways:
- Discrete Frequency Distribution
- Continuous Frequency Distribution