**Important Facts and Formulae**

**1.** Average or arithmetic mean is defined as sum of n different data divided by n.

Average = ${\frac{Sum\quad of\quad Observations}{Number\quad of\quad Observations}}$

**2.** Average Speed:- If a person travels a distance at a speed of x km/hr and the same distance at a speed of y km/hr then average speed during whole journey is ${\frac{2xy}{x+y}}$ km/hr

**3.** Average of first n natural number is Average = ${\frac{n (n+1)}{2n}=\frac{n+1}{2}}$

**4.** If average of some numbers is 'x' and a constant number 'a' is added to each term of the series.Then, new average = x + a

**5.** If average of some numbers is 'x' and a constant number 'a' is subtracted from each term of series. Then, new average = x-a

**6.** If average of some numbers is 'x' and each term of the series is multiplied by a constant number 'a'.Then, new average = ax

**7.** If average of some numbers is 'x' and each term of the series is divided by a constant number 'a'.Then, new average = x/a