Correct Answer - Option 2 : 9
Concept:
Mean: It is sum of all observations upon number of observations.
If x1, x2, x3, …., xn are the observations, then mean is given as
\(\rm \bar{X} = \frac{sum\ of\ observations}{number\ of\ observations}\)
\(\rm \bar{X}= \frac{x_{1}+x_{2}+...+x_{n}}{n}\)
Sum of first n natural number \(\rm = \frac{n(n+1)}{2}\)
Calculation:
We have X̅ = 5
Sum of first n natural number \(\rm = \frac{n(n+1)}{2}\)
Mean of first n natural number \(\rm = \frac{\frac{n(n+1)}{2}}{n}\)
\(\rm ⇒ 5 = \frac{(n+1)}{2}\)
⇒ 10 = n + 1
⇒ n = 9