Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2025
Exam
NDA
Year
2025
Subject
Mathematics
Chapter
Statistics

NDA 2025 · Mathematics · Statistics

What is the arithmetic mean of 8^2 , 9^2 , 10^2 , , 15^2 ?

What is the arithmetic mean of 828^2, 929^2, 10210^2, …\ldots, 15215^2?

Options

  1. A133.5133.5
  2. B135.5135.5
  3. C137.5137.5
  4. D139.5139.5

Correct answer

C. 137.5137.5

Step-by-step solution

The given sequence is 82,92,102,…,1528^2, 9^2, 10^2, \ldots, 15^2.

Number of terms, n=15−8+1=8n = 15 - 8 + 1 = 8.

Sum of the series S=∑k=815k2=∑k=115k2−∑k=17k2S = \sum_{k=8}^{15} k^2 = \sum_{k=1}^{15} k^2 - \sum_{k=1}^{7} k^2.

Using the formula ∑k=1nk2=n(n+1)(2n+1)6\sum_{k=1}^{n} k^2 = \dfrac{n(n+1)(2n+1)}{6},

∑k=115k2=15×16×316=1240\sum_{k=1}^{15} k^2 = \dfrac{15 \times 16 \times 31}{6} = 1240

∑k=17k2=7×8×156=140\sum_{k=1}^{7} k^2 = \dfrac{7 \times 8 \times 15}{6} = 140

S=1240−140=1100S = 1240 - 140 = 1100

Arithmetic mean =Sn=11008=137.5= \dfrac{S}{n} = \dfrac{1100}{8} = 137.5

Answer: 137.5137.5
Practice Statistics on Quantrex Academy →

More from Statistics

Let two lines of regression be x+y+11=0 and 2x+3y+4=0 for some data. What is the value of… NDA 2026Passage: The frequency distribution of marks obtained by 100 students in a certain… NDA 2026The standard deviation of 100 observations is 10 . If 5 is multiplied to each of the… NDA 2026Passage: The frequency distribution of marks obtained by 100 students in a certain… NDA 2026If the mean of 20 observations, namely x_1,x_2,x_3,…,x_ 20 is 1·414 , then what is the… NDA 2026If the random variable X has mean 3 and standard deviation 5 , then what is the variance… NDA 2026The standard deviation of 100 observations is 10. If 20 is added to each observation… NDA 2025Consider the following statements: I. Mean and variance have the same unit of… NDA 2025Consider the following for the four (04) items that follow: The frequency distribution of… NDA 2025Consider the following for the four (04) items that follow: The frequency distribution of… NDA 2025Consider the following for the two (02) items that follow: The sum and the sum of squares… NDA 2025The arithmetic mean of 100 observations is 50. If 5 is subtracted from each observation… NDA 2025The standard deviation of 100 observations is 10. If 5 is added to each observation and… NDA 2025Consider the following for the two (02) items that follow: The sum and the sum of squares… NDA 2025Consider the following for the four (04) items that follow: The frequency distribution of… NDA 2025The frequency distribution of the marks obtained by students in a Science examination is… NDA 2025 Full Statistics list Statistics JEE Maths PYQsJEE Mathematics PYQs All NDA PYQs