CUET PG 2023 — Mathematics PYQ

The original numbers are $x_1,x_2,x_3,\dots ,x_n$ where each $x_i=i$.

The new numbers, let's call them $y_i$, are formed by replacing each $x_i$ with $(i+1)x_i$:

Step 2: Calculate the Sum of New Numbers

The sum of the new set of numbers is:

Using the standard summation formulas:

1. Sum of squares: $\sum i^2=\frac{n(n+1)(2n+1)}{6}$

2. Sum of natural numbers: $\sum i=\frac{n(n+1)}{2}$

Now, add them together:

Take common factor $\frac{n(n+1)}{2}$:

Step 3: Find the New Mean

The mean is the total sum divided by the number of observations ($n$):