Testbook Logo
Exams SuperCoaching Test Series Skill Academy
More
English
Hindi

Question

Download Solution PDF

The mean of the series x1, x2...xn is x̅ If xn is replaced by k, then what is the new mean?

This question was previously asked in
NDA-II 2024 (Maths) Official Paper (Held On: 01 Sept, 2024)
Download PDF Attempt Online
View all NDA Papers >
  1. x̅ - xn + k
  2. \(\rm \frac{n\bar x-\bar x+k}{n}\)
  3. \(\rm \frac{\bar x-x_n-k}{n}\)
  4. \(\rm \frac{n\bar x-x_n+k}{n}\)

Answer (Detailed Solution Below)

Option 4 : \(\rm \frac{n\bar x-x_n+k}{n}\)
Free Tests
View all Free tests >
Free
BSF HC RO/RM All India Mega Live Test
5.4 K Users
100 Questions 200 Marks 120 Mins
Start Now

Detailed Solution

Download Solution PDF

Explanation:

Given:

\(\overline x = \frac{x_1+x_2+x_3+......... x_n}{n}\)

⇒ \(x_1+x_2+X_3+......x_n= n\overline x \)

⇒ Mean when xn is replaced by k

⇒ New mean = \(\frac{x_1+x_2+x_3+......... x_{n-1}+k}{n}\)

= \(\frac{n\overline x -x_n+k}{n}\)

∴ Option (d) is correct

Download Solution PDF
Latest NDA Updates

Last updated on May 30, 2025

->UPSC has released UPSC NDA 2 Notification on 28th May 2025 announcing the NDA 2 vacancies.

-> A total of 406 vacancies have been announced for NDA 2 Exam 2025.

->The NDA exam date 2025 has been announced for cycle 2. The written examination will be held on 14th September 2025.

-> Earlier, the UPSC NDA 1 Exam Result has been released on the official website.

-> The selection process for the NDA exam includes a Written Exam and SSB Interview.

-> Candidates who get successful selection under UPSC NDA will get a salary range between Rs. 15,600 to Rs. 39,100. 

-> Candidates must go through the NDA previous year question paper. Attempting the NDA mock test is also essential. 

‹‹ Previous Ques
Next Ques ››

More Measures of Central Tendency Questions

Q1.If a and b are non-negative real numbers such that a + 2b = 6, then the average of the maximum and minimum possible values of (a + b) is
Q2.If mean of X1, X2, X3, ..... Xn is X̅ then \(\rm \frac{\Sigma ^n}{e=1}(X_i-\bar X)\)= ?
Q3.If the ratio of mean and median of a distribution is 2 : 3 then the ratio of mode and mean is
Q4.The frequency of numbers 3, 5, 7 and 9 are X - 2, X + 2, X + 3 and 3 respectively. If the mean is 6.5 then the value of X:
Q5.What should the squares be like to find the mode from the formula.
Q6.The median of the data 3, 7, 2, 11, 4 and 9 is:
Q7.If for any data Σf = 40 and Σfx = 200 then the mean of that data is:
Q8.If the median of 1, 2, x, 4, 5 is 3 then its mean is
Q9.Mean of N numbers is X̅, the new mean when each number is multiplied by k is
Q10.The mean of five numbers is 18. If one number is removed the mean is 16. The number removed is

More Statistics Questions

Q1.Let a, b ∈ R. Let the mean and the variance of 6 observations –3, 4, 7, –6, a, b be 2 and 23, respectively. The mean deviation about the mean of these 6 observations is :
Q2.If a and b are non-negative real numbers such that a + 2b = 6, then the average of the maximum and minimum possible values of (a + b) is
Q3.If mean of X1, X2, X3, ..... Xn is X̅ then \(\rm \frac{\Sigma ^n}{e=1}(X_i-\bar X)\)= ?
Q4.If the ratio of mean and median of a distribution is 2 : 3 then the ratio of mode and mean is
Q5.Cumulative frequency table is required to find out which of the following.
Q6.The frequency of numbers 3, 5, 7 and 9 are X - 2, X + 2, X + 3 and 3 respectively. If the mean is 6.5 then the value of X:
Q7.What should the squares be like to find the mode from the formula.
Q8.The median of the data 3, 7, 2, 11, 4 and 9 is:
Q9.If for any data Σf = 40 and Σfx = 200 then the mean of that data is:
Q10.If the median of 1, 2, x, 4, 5 is 3 then its mean is
Suggested Test Series
View All >
Current Affairs (CA) 2025 Mega Pack for SSC/Railways/State Exam Mock Test
431 Total Tests with 4 Free Tests
Start Free Test
Current Affairs (CA) 2024 Mega Pack for SSC/Railways/State Exam Mock Test
427 Total Tests with   5 Free Tests
Start Free Test

More Mathematics Questions

Q1.log10 10000 = _______?
Q2.Consider a system equation \(2x+y-z=0\), \(4x - py + 4z = 4\) and \(x-y+z=q\) where \(p, q \in I\) and \(p, q \in [1, 10]\), then identify the correct statement(s).   List-I List-II (I) Number of ordered pairs \((p, q)\) for which system of equation has unique solution is (P) 1 (II) Number of ordered pairs \((p, q)\) for which system of equation has no solution is (Q) 9 (III) Number of ordered pairs \((p, q)\) for which system of equation has infinite solution is (R) 91 (IV) Number of ordered pairs \((p, q)\) for which system of equation has atleast one solution is (S) 90
Q3.Match List I with List II:   List - I List - II (I) The number of solutions of the equation\((1 - \cos 2x)(\cos 2x + \cot^2 x) = 0\) where \(0 \le x \le 2\pi\) is (P) 4 (II) \(\tan 81^\circ - \tan 63^\circ - \tan 27^\circ + \tan 9^\circ\) equals (Q) 3 (III) The number of solutions of (x, y), which satisfy |y| = sin x and y = cos-1(cos x), where -2π ≤ x ≤ 2π is (R) 2 (IV) For the equation \(\cos^{-1}x + \cos^{-1}2x + \pi = 0\), the number of real solutions is (S) 1     (T) 0  
Q4.If Σn = 36, find n
Q5.If log 2 = 0.2614, log 3 = 0.3521, log 6 = ?
Q6.The growth model for a population is Nt = N0ert where Nt is the population at time t, N0 is the initial population and r is the per capita growth rate. How long does it take for the population numbers to double?
Q7.Suppose that the growth rate of the number of individuals (N) in a population in an environment with a carrying capacity K is modelled as \(\frac{d N}{d t}=r N \frac{K-N}{K}\) where r is the per capita growth rate and t is time; r and K are positive constants. At which of the following values of N will the population growth rate be the maximum?
Q8.The shadow of a vertical pole, formed due to a nearby lamp which is at a height of 12 m, measures 4 m. If the lamp is moved horizontally 2 m further away from the pole, the length of the shadow measures 8 m. What is the height (in m) of the pole?
Q9.A pack of cards contains 4 aces, 4 kings, 4 queens and 4 jacks. Out of these 16 number of cards, two cards are drawn at random. Find the probability that at least one of them is an ace :
Q10.If the equations 2x2 + kx - 5 = 0 and x2 - 3x - 4 = 0 have one root common, then find the value of k.
Important Exams
SuperCoaching
Exams
Test Series
Previous Year Papers
Objective Questions
Testbook Edu Solutions Pvt. Ltd.
1st & 2nd Floor, Zion Building,
Plot No. 273, Sector 10, Kharghar,
Navi Mumbai - 410210
[email protected]
Toll Free:1800 833 0800
Office Hours: 10 AM to 7 PM (all 7 days)
Company
About usCareers We are hiringTeach Online on TestbookPartnersMediaSitemap
Products
Test SeriesTestbook PassOnline CoursesOnline VideosPracticeBlogRefer & EarnBooks
Our Apps
Follow us on
Copyright © 2014-2022 Testbook Edu Solutions Pvt. Ltd.: All rights reserved
User PolicyTermsPrivacy
Get Free Access Now
Hot Links： teen patti palace teen patti master update teen patti refer earn teen patti royal - 3 patti