Question:
Which one of the following is NOT a correct statement?
Which one of the following is NOT a correct statement?
Show Hint
Variance is always expressed in squared units, not in the same units as the data.
Updated On: Oct 18, 2025
- The standard deviation is greater than or equal to the mean deviation (about mean)
- The variance is expressed in the same units as the units of observation
- The value of standard deviation changes by a change of scale.
- The sum of squares of deviations is minimum when taken from the mean
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
The variance is the average of the squared deviations from the mean, so it is expressed in square units of the units of observation. Therefore, the statement that the variance is expressed in the same units as the units of observation is incorrect. The correct answer is option (b).
Step 1: Standard Deviation and Mean Deviation.
The standard deviation is always greater than or equal to the mean deviation. This is because the sum of the absolute deviations (mean deviation) is less than or equal to the square root of the sum of squared deviations (standard deviation).
Step 2: The Units of Variance.
Variance is calculated as the average of squared deviations, so its units are the square of the units of observation, unlike the standard deviation, which is in the same units as the data.
Step 3: Scale Effect on Standard Deviation.
The value of the standard deviation changes with scale. If we scale the data by a factor, the standard deviation is also scaled by the same factor.
Thus, the correct answer is option (b).
Was this answer helpful?
0
0
Top NIMCET Mathematics Questions
- Among the given numbers below, the smallest number which will be divided by 9, 10, 15 and 20 and leaves the remainders 4, 5, 10 and 15, respectively, is:
- If one AM (Arithmetic mean) \( a \) and two GM's (Geometric means) \( p \) and \( q \) be inserted between any two positive numbers, the value of \( p^3 + q^3 \) is:
- If one AM (Arithmetic mean) \( a \) and two GM's (Geometric means) \( p \) and \( q \) be inserted between any two positive numbers, the value of \( p^3 + q^3 \) is:
- A coin is thrown 8 times. What is the probability of getting a head in an odd number of throws?
- The value of \( \tan\left(\frac{\pi}{4} + \theta\right) \times \tan\left(\frac{3\pi}{4} + \theta\right) \) is:
View More Questions
Top NIMCET Probability and Statistics Questions
- The scores of students in a national level examination are normally distributed with a mean of 500 and a standard deviation of 100. If the value of the cumulative distribution of the standard normal random variable at 0.5 is 0.691, then the probability that a randomly selected student scored between 450 and 500 is:
- The number of accidents per week in a town follows a Poisson distribution with mean 2. If the probability that there are three accidents in two weeks time is \( k e^{-6} \), then the value of \( k \) is:
- The mean of 5 observations is 5 and their variance is 124. If three of the observations are 1, 2, and 6, then the mean deviation from the mean of the data is:
- The 10th and 50th percentiles of the observation 32, 49, 23, 29, 118 respectively are
- The first three moments of a distribution about 2 are 1, 16, -40 respectively. The mean and variance of the distribution are
Top NIMCET Questions
- How much work is done to slide a crate for a distance of 25 m along a loading dock by pulling on it with a 180 N force where the dock is at an angle of \(45^\circ\) from the horizontal?
- Let \( f : \mathbb{R} \to \mathbb{R} \) be a function such that \( f(0) = \frac{1}{\pi} \) and \( f(x) = \frac{x}{e^x - 1} \) for \( x \ne 0 \). Then:
- The value of the limit \[ \lim_{x \to 0} \left( \frac{1^x + 2^x + 3^x + 4^x}{4} \right)^{\frac{1}{x}} \] is:
- Consider the function \( f(x) = x^{2/3} \cdot (6 - x)^{1/3} \). Which of the following statements is false?
- Lines \( L_1, L_2, \dots, L_{10} \) are distinct, among which the lines \( L_2, L_4, L_6, L_8, L_{10} \) are parallel to each other, and the lines \( L_1, L_3, L_5, L_7, L_9 \) pass through a given point \( C \). The number of points of intersection of pairs of lines from the complete set \( L_1, L_2, L_3, \dots, L_{10} \) is:
View More Questions