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
NDA 01/2025: English Subject Test
5.5 K Users
30 Questions 120 Marks 30 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 Jun 18, 2025

->UPSC has extended the UPSC NDA 2 Registration Date till 20th June 2025.

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

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

-> 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.The mean of the series x1, x2...xn is x̅ If xn is replaced by k, then what is the new mean?
Q2.The mean of n observations 1, 4, 9, 16 ...., n2 is 130. What is the value of n?
Q3.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
Q4.If mean of X1, X2, X3, ..... Xn is X̅ then \(\rm \frac{\Sigma ^n}{e=1}(X_i-\bar X)\)= ?
Q5.If the ratio of mean and median of a distribution is 2 : 3 then the ratio of mode and mean is
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

More Statistics Questions

Q1.The mean of the series x1, x2...xn is x̅ If xn is replaced by k, then what is the new mean?
Q2.Let \(\rm \Sigma_{i=1}^9x_i^2=885\) If M is the mean and σ is the standard deviation of  x1, x2, x3.....x9 then what is the value of M2 + σ2?
Q3.What is the mean deviation of the first 10 natural numbers?
Q4.The mean of n observations 1, 4, 9, 16 ...., n2 is 130. What is the value of n?
Q5.Let x - 3y + 4 = 0 and 2x - 7y + 8 = 0 be two lines of regression computed from some bivariate data. If byx and bxy are regression coefficients of lines of regression of y on x and x on y respectively, then what is the value of bxy + 7byx?
Q6.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 :
Q7.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
Q8.If mean of X1, X2, X3, ..... Xn is X̅ then \(\rm \frac{\Sigma ^n}{e=1}(X_i-\bar X)\)= ?
Q9.If the ratio of mean and median of a distribution is 2 : 3 then the ratio of mode and mean is
Q10.Cumulative frequency table is required to find out which of the following.

More Mathematics Questions

Q1.If cosec θ + cot θ = p, then \(\rm\frac{p^2-1}{p^2+1}\) equal:
Q2.In a binomial distribution, if the mean is 6 and the standard deviation is √2, then what are the values of the parameters n and p respectively?
Q3.Three perfect dice D1, D2 and D3 and are rolled. Let x, represent the numbers on D1, D2 and D3 respectively. What is the number of possible outcomes such that x < y < z?
Q4.Three perfect dice are rolled. Under the condition that no two show the same face, what is the probability that one of the faces shown is an ace (one)?
Q5.The occurrence of a disease in an industry is such that the workers have 20% chance of suffering from it. What is the probability that out of 6 workers chosen at random, 4 or more will suffer from the disease?
Q6.Two perfect dice are thrown. What C is the probability that the sum of the numbers on the faces is neither 9 nor 10?
Q7.Urn A contains 2 white and 2 black balls while urn B contains 3 white and 2 black balls. One ball is transferred from urn A to urn B and then a ball is drawn out of urn B. What is the probability that the ball is white?
Q8.A fair coin is tossed till two heads occur in succession. What is the probability that the number of tosses required is less than 6?  
Q9.The mean of the series x1, x2...xn is x̅ If xn is replaced by k, then what is the new mean?
Q10.Let \(\rm \Sigma_{i=1}^9x_i^2=885\) If M is the mean and σ is the standard deviation of  x1, x2, x3.....x9 then what is the value of M2 + σ2?
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 gold teen patti star teen patti master downloadable content