Question

Find the mean of all natural numbers from 32 to 46. Find the new mean when each number is diminished by 5. 

Answer 1

The numbers are: 
32, 33, 34, 35, 36, 37' 38, 39, 40, 41, 42, 43, 44, 45, 46 

`barx = (x_1 + x_2 + x_3 + .... + x_n)/n`

n = 15

⇒ `barx = (32+33+34+35+36+37 +38+39+40 + 41 +42+43+44+45+46 )/15`

⇒ `barx = 585/15`

⇒ `barx = 39`

Therefore, Mean of natural numbers from 32 to 46 = 39 

If numbers are diminished by 5, the numbers are: 
27 ,28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,41 

`barx = (x_1 + x_2 + x_3 + .... + x_n)/n`

n = 15

⇒ `barx = (27 +28+29+30 + 31 +32+33+34+35+36+37 +38+39+40 + 41 )/15`

⇒ `barx = 510/15`

⇒ `barx = 34`

Therefore, Mean of odd numbers from 5 to 20 when diminished by 5= 34