SSC CGL (Prelims) Maths: Statistics questions with solutions

Q1. A class of 30 students appeared in a test. The average score of 12 students is 62, and that of the rest is 74. What is the average score of the class?

1. 70.2
2. 69.2
3. 68.2
4. 67.2

Answer: 69.2

The first 12 students have total marks $12\times 62=744$. The remaining 18 students have total marks $18\times 74=1332$. The class total is 2076, so the average is $2076/30=69.2$.

Q2. The average of the squares of the first 45 natural numbers is:

1. 698.67
2. 699.67
3. 697.67
4. 696.67

Answer: 697.67

The sum of squares of the first $n$ natural numbers is $\frac{n(n+1)(2n+1)}{6}$. For $n=45$, the sum is $\frac{45\cdot46\cdot91}{6}=31395$, and the average is $31395/45=697.67$.

Q3. What is the median of the following numbers: 7, 9, 12, 15, 19?

1. 9
2. 12
3. 13
4. 15

Answer: 12

The numbers are already in ascending order. Since there are 5 numbers, the median is the 3rd number, which is 12.