Coefficient of Variation
Statistics
6
JEE Qs
8%
Hard
40
min
Always use Coefficient of Variation for comparing the consistency or variability of two distributions, especially when their means are different or units are incomparable.
🧮 Key Formulas
✅ Key Points for JEE
- 1Coefficient of Variation (CV) is a relative measure of dispersion, expressed as a percentage, which allows for comparison of variability across different datasets.
- 2A dataset with a smaller CV is considered more consistent or less variable than a dataset with a larger CV.
- 3CV is dimensionless, making it suitable for comparing data sets that have different units or significantly different means.
- 4If each observation in a data set is multiplied by a positive constant 'k', both the mean and standard deviation are multiplied by 'k', resulting in an unchanged CV.
- 5If a constant 'a' is added to each observation, the mean changes by 'a' but the standard deviation remains unchanged, thereby altering the CV.
⚠️ Common Mistakes
- ✕Incorrectly using only standard deviation to compare variability of two datasets, especially when their means are significantly different.
- ✕Making calculation errors in determining the mean or standard deviation, which directly propagate to an incorrect CV.
- ✕Forgetting to multiply by 100 to express the Coefficient of Variation as a percentage, leading to misinterpretation of the result.
- ✕Not understanding how data transformations (adding or multiplying constants to observations) affect the mean, standard deviation, and consequently the CV.
📝 Practice Questions
See allQ1. Let x1, x2, … , x10 be ten observations such that ∑10i=1 (xi −2) = 30, ∑10i=1 (xi −β)2 = 98, β > 2, and their variance is 4 . If μ and σ2 are respectively the mean and the variance of 2 (x1 −1) + 4β , 5 2 (x2 −1) + 4β, … . , 2 (x10 −1) + 4β , then βμσ2 is equal to : (1) 100 (2) 120 (3) 110 (4) 90
Q11.The area of the region {(x, y) : x2 + 4x + 2 ≤y ≤|x + 2|} is equal to (1) 7 (2) 5 (3) 24/5 (4) 20/3
Q5. Marks obtains by all the students of class 12 are presented in a freqency distribution with classes of equal width. Let the median of this grouped data be 14 with median class interval 12-18 and median class frequency 12 . If the number of students whose marks are less than 12 is 18 , then the total number of students is (1) 52 (2) 48 (3) 44 (4) 40
Q86. X α 1 0 −3 Let the mean and the standard deviation of the probability distribution be μ and σ, P(X) 31 K 16 41 respectively. If σ −μ = 2, then σ + μ is equal to________ JEE Main 2024 (05 Apr Shift 2) JEE Main Previous Year Paper
Q69.If the mean of the following probability distribution of a random variable X : X 0 2 4 6 8 46 is , then the variance of the distribution is P(X) a 2a a + b 2b 3b 9 (1) 173 (2) 566 27 81 (3) 151 (4) 581 27 81
Q69.Consider 10 observation 𝑥1, 𝑥2, . .. 𝑥10, such that ∑𝑖=10 1 𝑥𝑖−𝛼= 2 and ∑𝑖=10 1 𝑥𝑖−𝛽2 = 40, where 𝛼, 𝛽 are 6 84 𝛽 positive integers. Let the mean and the variance of the observations be and respectively. The is equal to: 5 25 𝛼 (1) 2 (2) 3 2 (3) 5 (4) 1 2
NCERT Chapters
- Class 11 Mathematics Ch 15: Statistics