Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2024
Exam
NDA
Year
2024
Subject
Mathematics
Chapter
Statistics

NDA 2024 · Mathematics · Statistics

Let ∑_ i=1 ^9 x_i^2=855 . If M is the mean and σ is the standard...

Let ∑i=19xi2=855\sum_{i=1}^9 x_i^2=855. If M is the mean and σ\sigma is the standard deviation of x1,x2,…..x9x_1, x_2, \ldots.. x_9, then what is the value of M2+σ2?\mathrm{M}^2+\sigma^2 ?

Options

  1. A100
  2. B95
  3. C90
  4. D85

Correct answer

B. 95

Step-by-step solution

Given that ∑i=19x12=855\sum_{\mathrm{i}=1}^9 \mathrm{x}_1{ }^2=855 We know that variance (62)=∑i=19x12N−( Mean )2\left(6^2\right)=\frac{\sum_{i=1}^9 x_1{ }^2}{\mathrm{ N}}-(\text{ Mean })^2⇒62=8559−M2⇒62+M2=8559=95\begin{aligned} & \Rightarrow \quad 6^2=\frac{855}{9}-\mathrm{M}^2 \\ & \Rightarrow \quad 6^2+\mathrm{M}^2=\frac{855}{9}=95 \end{aligned}$$
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