if the no of observations are reduced by 75% and the average remains the same what is the change in - Maths - Statistics

Question

if the no of observations are reduced by 75% and the average
remains the same what is the change in the values?

Lovina Kansal · Accepted Answer

Dear student
We know that if x1,x2,x3,
xn  are n values of a variable X, then the average isdenoted by  X¯ is defined asX¯= x1+x2+x3+
+xnn=1n∑i=1nxi    
(1)Now, if number of observations gets reduced by 75% ie n-75100n ie it will becomen4and given that mean Remains the sameThen eq(1) becomesX¯=1n/4∑i=1nxi ⇒X¯=1n∑i=1n4xi i,e set of observations will become increase by 4 times
Regards

if the no of observations are reduced by 75% and the average remains the same what is the change in the values?