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

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NDA-II 2024 (Maths) Official Paper (Held On: 01 Sept, 2024)
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  1. x̅ - xn + k

Answer (Detailed Solution Below)

Option 4 :
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Detailed Solution

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Explanation:

Given:

⇒ 

⇒ Mean when xn is replaced by k

⇒ New mean = 

= 

∴ Option (d) is correct

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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:
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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
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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?
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