Mean Deviation — About mean, median
Statistics
6
JEE Qs
8%
Hard
75
min
Always perform calculations for mean or median accurately for the given data type (ungrouped, discrete, or continuous) first, and consistently apply the absolute value for deviations.
🧮 Key Formulas
✅ Key Points for JEE
- 1Mean deviation is always calculated using the absolute value of deviations, which ensures that distances from the central value are treated as positive.
- 2The mean deviation about the median is always less than or equal to the mean deviation about any other point, making it the minimum mean deviation for a given dataset.
- 3For grouped data (discrete or continuous frequency distributions), the frequency (fᵢ) of each observation or class interval must be multiplied with the absolute deviation before summation.
- 4When dealing with continuous frequency distributions, use the midpoints of the class intervals (xᵢ_mid) to represent the observations for calculating deviations.
- 5The coefficient of mean deviation is a relative measure of dispersion, allowing for comparison of variability between datasets that might have different units or widely differing means/medians.
⚠️ Common Mistakes
- ✕Forgetting to take the absolute value of deviations (|xᵢ - A|), which is a fundamental error leading to incorrect or zero mean deviation.
- ✕Errors in the initial calculation of the mean or median, especially for grouped data, as these values are foundational for all subsequent calculations.
- ✕Incorrectly calculating the median for continuous frequency distributions, by misidentifying the median class or using wrong values for L, C, f, or h.
- ✕Applying formulas for ungrouped data to grouped data, or vice versa, without proper modification to include frequencies (fᵢ).
📝 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