lecture 6

Question 1

what is sample mode

Answer 1

most frequently observed value

Question 2

what is sample mode if all obs occur once

Answer 2

every value is a mode
or
none of values is a mode
usually this is the case but if have rounded whole number = can have same number twice

Question 3

what can a set of obs be

Answer 3

unimodal or mutimodal

Question 4

give mode of
8, 1, 5, 2, 6, 2, 9, 8

Answer 4

8 and 2 repeated twice = both are modes
data bimodal

Question 5

what are measures of central tendency

Answer 5

mean, median, mode
descriptive or summary stats, location of measurement on axis of data

Question 6

compare mean median and mode

Answer 6

mean = uses all obs directly, sensitive to extreme obs
median = uses all obs indirectly (not all data values used), not sensitive to extreme obs
mode= rarely used in practice

Question 7

what are measures of variability or spread

Answer 7

range
variance and standard deviation
Interquartile range

Question 8

why are measures of central tendency not enough

Answer 8

not a Sufficient description of data
also need to know how spread out obs are around the center
compare spreads of samples

Question 9

what is sample range

Answer 9

R= Xl-Xs
(largest minus smallest value)
extremely crude measures of spread
range affected by extreme obs

Question 10

what is sample variance

Answer 10

s^2
(1/n-1) sum of (Xi-Xbar)^2

Question 11

what is standard deviation

Answer 11

defined as sqrt s^2
Square root of sample variance
often used bc measured in same units as obs (original measurements)

Question 12

final formula of sample variance

Answer 12

s^2 = 1/n-1 sum of (Xi-Xbar)^2
n-1 = degrees of freedom
can expand and get
sum of Xi^2 - n Xbar^2
and substitute using
Xbar = 1/n sum of Xi
so sum of Xi^2 - sum of Xi^2/n
need sum of squared values and sum of values squared only
can use any formula