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

2022
Views:

88

Pages:

2
Author:

Niklas

LECTURE 5 How to display a variable? 1 variable 2 variable histogram bar plot bar plot side by side Sum up the data [A table of data] Graphical representation * summarize data → many basic info * the modal class is the highest density Tools available to summarize data central density variability shape Example: how difficult is the exam [A histogram] The median 1 See if you can ordinate the data 2 sort the data from the lowest to the highest N+1 M = 2 position of the median Example 1,2,5,1,6,8 0,1,2,5,6,8 N=7, m=3+1=4 Odd N 1,2,5,1,6,8,3 0,1,1,2,3,5,6,8 N=8, m=2+1=3 Even N \[\frac{2+3}{2}=2.5\] Quantile Q_a is the value that leaves to its left a fraction a% of the data. Q_a and a fraction (1-a)% to its right. median is a quantile of level 0.5 - most used also the first quartile Q_1 = Q_0.25 and the third quartile Q_3 = Q_0.75 Example 0,1,1,3,5, 40, 42, 20, 30, 35 N=11 mode = 1 median = Q_2 = Q_0.5 = 5 Q_1 = Q_0.25 = (N+1)/4 = 3 Q_3 = Q_0.75 = (N+1)/4 * 3 = (N+1) * 0.75 = 9 Exercise N=80, m=(N+1)/2 = 40.5 between 174, 175 → 174.5 Q_1 = 20 position → 165 Q_3 = 3 * (N+1)/4 = 61 → 180 The median is the middle value of the observations when the observations are ordered from the smallest to the largest The mean is the sum of the observations divided by the number of observations. It is interpreted as the balance point of the distribution. It refers to the averaging, that is, adding up the data points and dividing by how many there are