University:
York University
Course:
MATH 1131 | Introduction to Statistics I
Academic year:

2022
Views:

444

Pages:

3
Author:

Niklas

LECTURE 6 Arithmetic mean - most common used also called average Example: height N=80 m=13851/80 173 (16.5) Mean and Median - Median produces a sort of balance, with half of the units before the median, and half after it. It is not important how far they are - Mean is instead the centroid, like a physical concept, it balances the masses related to the observations Conditional and marginal measures The central tendency measures for conditional variables are, for simplicity, labeled as conditional central tendency measures, to distinguish them from the central tendency measures calculated on the variable not conditional, that is marginal Sometimes, even starting from raw data, there may be ambiguities in the calculation of the measures. More generally, the data can be provided in aggregate form. Example x 0-10 10-20 20-30 n 5 10 15 v 15 15 15 N 12 f 0.33 0.66 1 v.f 1.65 10 15 mean=25+150+150/15 mean=195/15=11.65 Example Y = high school mark X = sex, assuming modalities X₁ = M, X₂ = F N₁ = 41 N₂ = 39 different sizes N = 80 Group means: Y₁ = 3183 / 41 = 77.63 Y₂ = 3087 / 39 = 79.15 General mean: Ȳ = (N₁Y₁ + N₂Y₂) / N = (41 * 77.63 + 39 * 79.15) / 80 = 78.38 Exercise Female Male 5 6 7 8 9 6 7 8 9 10 15 16 16 16 16 18 14 2 4 39 41 Conditional mean (F): (5 + 6 + 7 + 8 + 9 + 2) / 6 = 291 / 39 = 7.46 Conditional mean (M): (5 + 6 + 6 + 7 + 8 + 9 + 10 + 16 + 16 + 16 + 16 + 14) / 11 = 301 / 41 = 7.34 Marginal mean: (5 + 6 + 10 + 31 + 8 + 2 + 14 + 6) / 80 = 7.40 Range An intuitive measure of the variability of a set of data is the difference (distance) between minimum and maximum Same range Range = Y(N) - Y(1) Interquartile range (IQR) the difference (distance) between quartiles IQR = Q₃ - Q₁