Key Concepts
- 1Mean (direct method)
- 2Mean (assumed mean)
- 3Mean (step deviation)
- 4Mode formula (grouped)
- 5Median formula (grouped)
- 6Empirical relation
- 7Ogive (cumulative frequency curve)
- 8Modal class
- 9What is the formula for the mean of grouped data using the direct method?
- 10What is the step-deviation method for finding the mean?
Important Formulas & Facts
Mean = Σfᵢxᵢ / Σfᵢ
Mean = a + Σfᵢdᵢ/Σfᵢ where dᵢ = xᵢ - a
Mean = a + (Σfᵢuᵢ/Σfᵢ) × h where uᵢ = (xᵢ-a)/h
Mode = l + [(f₁-f₀)/(2f₁-f₀-f₂)] × h
Median = l + [(n/2 - cf)/f] × h
3 Median = Mode + 2 Mean
Less-than ogive: rising curve. More-than ogive: falling curve. Intersection gives median.
The class with the highest frequency.
Mean = (Sum of f_i * x_i) / (Sum of f_i), where f_i is the frequency and x_i is the class mark (midpoint) of each class.
Mean = a + h * (Sum of f_i * u_i) / (Sum of f_i), where u_i = (x_i - a)/h, a is the assumed mean, and h is the class width.
Must-Know Questions
Q1Median of 2, 3, x, 7, 9 (ascending) is 5. Find x.
n = 5. Median = 3rd value = x = 5.
Q2The empirical relationship between mean, median and mode:
3 Median = Mode + 2 Mean.
Q3An ogive represents:
An ogive is the graph of cumulative frequency distribution.
Q4Mean of x, x+2, x+4, x+6, x+8 is 11. Find x.
(5x + 20)/5 = x + 4 = 11. x = 7.
Q5If mean of distribution is 6, find p: x: 2,4,6,10,p+5; f: 3,2,3,1,2.
Σfx = 6+8+18+10+2(p+5) = 52+2p. Σf = 11. Mean = (52+2p)/11 = 6. 52+2p = 66. p = 7.
Practice Statistics
Reinforce what you just revised with practice questions