The variance of 10 observations is 25. If 2 is multiplied to each of the observations and subsequently 7 is subtracted from each multiplied observation, then what is the new variance?
100
If each observation is transformed as \(Y=2X-7\), the variance scales by the square of the multiplying constant while the subtracted constant has no effect: \(\text{Var}(Y)=2^{2}\,\text{Var}(X)\). With \(\text{Var}(X)=25\), the new variance is \(4\times25=100\).
Similar Questions
Mean of 100 observations is 50 and standard deviation is 10. If 5 is added to each observation, then what will be the new mean and new standard deviation respectively?
If \(\rm \displaystyle \sum_{i = 1}^{10}x_i = 110\) and \(\rm \displaystyle \sum_{i = 1}^{10}x_i^2 = 1540\) then what is the variance?
The sum of deviations of n numbers from 10 and 20 are p and q respectively. If (p - q)2 = 10000, then what is the value of n?
In any discrete series (when all values are not same) if x represent mean deviation about mean and y represent standard deviation, then which one of the following is correct?
If V is the variance and M is the mean of first 15 natural numbers, then what is V + M 2equal to?
Which one of the following subjects shows highest variability of marks ?
What is the coefficient of variation of marks in Mathematics ?
Arithmetic mean of 10 observations is 60 and sum of squares of deviations from 50 is 5000. What is the standard deviation of the observations?
Consider the following statements:
1) If 10 is added to each entry on a list, then the average increases by 10
2) IF 10 is added to each entry on a list, then the standard deviation increases by 10
3) if each entry on a list is doubled then the average doubles
What of the above statements are correct?
The variance of 25 observations is 4. If 2 is added to each observation, then the new variance of the resulting observations is
Important Questions from Variance and Standard Deviation
Mean of 100 observations is 50 and standard deviation is 10. If 5 is added to each observation, then what will be the new mean and new standard deviation respectively?
When sampling is done without replacement then standard error of mean is:
Consider a population that is finite, and sampling is with replacement. If the variance of the population is 2176.8 with a sample size of 16, then the variance of the sampling distribution of means is:
If \(\rm \displaystyle \sum_{i = 1}^{10}x_i = 110\) and \(\rm \displaystyle \sum_{i = 1}^{10}x_i^2 = 1540\) then what is the variance?
The sum of deviations of n numbers from 10 and 20 are p and q respectively. If (p - q)2 = 10000, then what is the value of n?
