Sep25
Table of Contents
1. Standard Deviation - average variablity around the mean
- how far the numbers are away from the mean
- the farther they are the higher the deviation
population:
- n (size)
- u (mean)
sample:
- n (size)
- u (mean)
ex: population: 13, 14, 15, 16, 17 (hours); u = 15, n = 5 bar plot with mean as midpoint and calculate the distance from each point to midline. numbers: 2, 1, 1, 2, 0 now square them… numbers2: 4 + 1 + 1 + 4 + 0 = 10 standard deviation2 = 10/5 = 2hrs2 standard deviation -> sqrt(2hr2) = 1.41 formula: standard deviation = sqrt((xi - u)2)/n)
WARNING! can only use standard deviation when the mean is GOOD.
- bellshape
2. Interquartile Range (IQR) - the spread or range of the middle 50% data
- IQR = Q3 - Q1
- each side of the box has the same amount of data
- Q1 - 25th percentile
- Q2 - 50th percentile
- Q3 - 75th percentile
EX: data: 6, 12, 14, 15, 20, 21, 22, 24, 28, 36, 40 6–25%–Q1: 14(25%) | Q2: 21 | Q3: 28(25%)–25%–40 IQR = 28-14 = 14 Lower fence: Q1 - 1.5*IQR = 14 - 21 = -7 Upper Fence: Q3 + 1.5*IQR = 28 + 21 = 49
WARNING! can only use IQR when the median is GOOD.
- skewed left