Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Statistics

NDA 2021 · Mathematics · Statistics

For the set of numbers x, x, x+2, x+3, x+10 where x is a natural...

For the set of numbers x,x,x+2,x+3,x+10x, x, x+2, x+3, x+10 where xx is a natural number, which of the following is/are correct? 1. Mean > Mode 2. Median > Mean Select the correct answer using the code given below.

Options

  1. A1 only
  2. B2 only
  3. CBoth 1 and 2
  4. DNeither 1 nor 2

Correct answer

A. 1 only

Step-by-step solution

Natural numbers : x⋅x,x+2,x+3,x+10x \cdot x, x+2, x+3, x+10 Mode = Most number of times repeated number ∴\therefore Mode =x→=x\rightarrow Mean of the numbers,  Mean =x+x+x+2+x+3+x+105xˉ=5x+155=x+3\begin{aligned} & \text{ Mean }=\frac{x+x+x+2+x+3+x+10}{5} \\ & \bar{x}=\frac{5 x+15}{5}=x+3 \end{aligned} Median of the numbers, Numbers in ascending order : x,x,x+2,x+3,x+10n=5 (i.e. odd numbers) M=(n+12)th  observation =(5+12)th  observation =3rd  observation ∴M=x+2\begin{aligned} & x, x, x+2, x+3, x+10 \\ & n=5 \text{ (i.e. odd numbers) } \\ & \mathrm{M}=\left(\frac{n+1}{2}\right)^{\text{th }} \text{ observation } \\ & =\left(\frac{5+1}{2}\right)^{\text{th }} \text{ observation }=3^{\text{rd }} \text{ observation } \\ & \therefore \mathrm{M}=x+2 \end{aligned} Hence, Mean > Median > Mode
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