lecture 7

Question 1

what must we be careful with with sample variance

Answer 1

rounding
if round mean = can get a negative variance which is impossible
so be careful

Question 2

what do we need to describe a data set

Answer 2

provide
numerical measures of center = mean, median, mode
Numerical measures of spread = range, variance
we must describe distribution of values or obs in sample
can be symmetric around a central point but not always

Question 3

describe symmetric distributions

Answer 3

Sample have perfectly symmetric distribution if its histogram has a symmetric shape around some x value
mean = median

Question 4

how often does sample have perfectly symmetrical distribution

Answer 4

RARE
in some cases approximation pretty good
so mean ~ median
around the same
Unlikely they are numerically exactly the same - more possible for a population

Question 5

how can data be skewed

Answer 5

left or right skew
depends on where tail is = away from central, where freq of obs low

Question 6

describe right skew

Answer 6

positively right skewed data = histogram shows long tail on right
median < mean
mean moves to right
right tail dominating
not outliers tho, since like slowly drags out tail

Question 7

describe left skew

Answer 7

negatively left skewed data = histogram shows long tail on left
median>mean
mean pulled to left bc directly influenced by data

Question 8

can we compete sample mean, median and variance if we only see histogram

Answer 8

nooo
data grouped in intervals
by looking at height we can see how many obs in interval but do not know exact location within each - hard to make precise conclusions only rough calculations
only approx
also cannot draw inferences

Question 9

from samples to populations

Answer 9

data representative of some underlying population
real goal is to understand characteristics of population based on sample

Question 10

corresponding population quantities - things we measure

Answer 10

sample mean = Xbar –> pop mean = μ
sample variance = s^2 –> pop variance = σ^2
Sample standard dev = s –> pop stand dev (s.d.) = σ

Question 11

what does sample have to be

Answer 11

representative of population

Question 12

how to think about population - interpretation

Answer 12

as sample with extremely large sample size
keep collecting data until learnt everything about way data generated
Very large, infinite sample size= we have learnt everything we possibly could learn
Ultimately - histogram where bins gets smaller and smaller until it becomes a nice curve