Question:
If the mean deviation of a distribution is 20.20, the standard deviation of this distribution is :
If the mean deviation of a distribution is 20.20, the standard deviation of this distribution is :
Show Hint
Use the empirical relation QD : MD : SD = 10 : 12 : 15, so SD = (5/4) x MD.
Updated On: Jul 4, 2026
- 15.15
- 25.25
- 30.39
- None of these
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Recall the standard empirical relationship among the three common measures of dispersion, namely quartile deviation (QD), mean deviation (MD) and standard deviation (SD), when the distribution is reasonably symmetric (moderately normal).\[QD : MD : SD = 10 : 12 : 15\]
Step 2: From this ratio, mean deviation and standard deviation are related as\[MD = \frac{12}{15} SD = \frac{4}{5} SD\]
Step 3: Rearrange to express SD in terms of MD.\[SD = \frac{5}{4} MD\]
Step 4: Substitute the given mean deviation \(MD = 20.20\).\[SD = \frac{5}{4} \times 20.20 = 1.25 \times 20.20 = 25.25\]
Step 5: So the standard deviation of the distribution is 25.25, which matches option (B).
Was this answer helpful?
0
0
Top CPET Statistics Questions
- The statements below relate to Bayes theorem in probability:
(i) Bayes theorem gives a formula to compute conditional probability.
(ii) The posterior probability computed by Bayes theorem supersedes the prior probability.
(iii) Bayes theorem can be used to compute probabilities of past events on the basis of the occurrences of subsequent events.
Identify the correct answer: - If \(P(A) = 0.25\), \(P(B|A) = 0.5\), \(P(B|\bar{A}) = 0.75\) then \(P(A|B)\) is ______.
- Three functions \(F_1(x)\), \(F_2(x)\) and \(F_3(x)\) are defined below:
(i) \(F_1(x) = 0\), for all \(x \in (-\infty, +\infty)\)
(ii) \(F_2(x) = 1\), for all \(x \in (-\infty, +\infty)\)
(iii) \(F_3(x) = 0\), for all \(x \le 0\) and \(F_3(x) = 1\), for all \(x > 0\)
Which of the above functions is a distribution function of a random variable? - If a random variable \(X\) has mean 3 and standard deviation 5, then the variance of \(Y = 2X - 5\) is:
- Three numbers \(X\), \(Y\), \(Z\) are randomly drawn from the set \(\{1, 2, 3, 4\}\). \(E(XYZ)\) is equal to:
View More Questions
Top CPET Questions
- Which of the following is a key reason for choosing DRAM over SRAM for main memory?
- Which of the following components in an FPGA is responsible for implementing combinational and sequential logic?
- What is the main purpose of declaring a base class as virtual in multiple inheritance?
- What happens if a class contains at least one pure virtual function?
- What happens if a derived class defines a function with the same name as a base class function, but with a different parameter list?
View More Questions