Discussion
The mean of the distribution in which the value of x are 1, 2 ...... n. The frequency of each being unity is :
Answer: C
The mean is \(\frac{(n+1)}{2}\).
Each value from 1 to n occurs once, so the mean is the sum of the first n natural numbers divided by n:
\[ \begin{aligned} \bar{x} &= \frac{1 + 2 + \dots + n}{n} \\ &= \frac{n(n+1)/2}{n} = \frac{n+1}{2} \end{aligned} \]
For n = 5 that gives (1 + 2 + 3 + 4 + 5)/5 = 3 = 6/2.
\(\frac{n(n+1)}{2}\) is the sum, not the mean: it forgets to divide by n. \(\frac{n}{2}\) and \(\frac{(n-1)}{2}\) are each half a unit off, as the n = 5 check shows (2.5 and 2).
No comment is present. Be the first to comment.
Loading…
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development