Question:

If the mean deviation about the mean of the numbers 1, 2, 3, …. n, where n is odd, is 5(n+1)n\frac{5(n + 1)}{n}, then n is equal to ______.

Updated On: Sep 24, 2024
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Correct Answer: 21

Solution and Explanation

The correct answer is: 21

Mean

=n(n+1)2n=n+12=\frac{\frac{n(n+1)}{2}}{n}=\frac{n+1}{2}

⇒((n−1)+(n−3)+(n−5)+...0=5)=5(n+1)⇒((n-1)+(n-3)+(n-5)+...0=5)=5(n+1)

⇒(n+14)(n−1)=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:

  1. Discrete Frequency Distribution
  2. Continuous Frequency Distribution