NIMCET 2021 — Mathematics PYQ

The Arithmetic Mean ($\bar{x}$) for a frequency distribution is given by the formula:

Step 1: Identify the values and frequencies.

• Values ($x_i$): $0,1,2,\dots ,n$ (where $n=50$)

• Frequencies ($f_i$): ${}^n{C}_0{,}^n{C}_1{,}^n{C}_2,\dots {,}^n{C}_n$

Step 2: Calculate the sum of frequencies ($\sum f_i$).

The sum of binomial coefficients is a standard identity:

For $n=50$:

Step 3: Calculate the sum of products ($\sum f_i{x}_i$).

We need to find the value of:

Using the property $r\cdot {}^n{C}_r=n\cdot {}^{n-1}{C}_{r-1}$:

For $n=50$:

Step 4: Calculate the Arithmetic Mean.

Final Answer:

The Arithmetic Mean (AM) is $25$.