101 students took an exam. Each received a distinct integer grade from 0 to 100, inclusive.

Mean of the grades?

(I think there is a formula and I’ve forgotten it. Please help!)

101 students took an exam. Each received a distinct integer grade from 0 to 100, inclusive.

Mean of the grades?

(I think there is a formula and I’ve forgotten it. Please help!)

The possible scores are distinct integers which range from 0 to 100. As the question implies there are **101 unique scores given to all 101 students which range from 0-100.**

**Question is asking to find the mean, which is sum of the total scores (0 to 100) upon number of students (101).**

We essentially just have to calculate the sum of numbers from 0 to 100 and divide it by 101.

- Sum of 0 to 100 =
**N(N+1) by 2**= (100*101)/2 = 5050 - Taking the Sum from above and dividing it by number of students = 5050/101 =
**50.**

hence **50** should be the Mean of the scores from 0 to 100 for 101 students each with distinct scores.

Additionally, you can also use formula of Arithmetic progression for similar questions where the difference between two terms is constant but unlike this problem, is greater than 1.

Sum of **n** terms where **a** is the first term and **d** is the constant difference = **(n/2) * (a + a + (n-1)d)** a.k.a. **(n/2)*(a + an)** since a + (n-1)d is the formula to find the nth term. This form is basically how we calculated the question in the first place with the prettier looking formula i.e. **N(N+1) by 2**

Hope this helps.

Jeet

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It certainly does.

Thanks, Jeet!

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