Question

Describe the relationship between bias and variability through an example. Given that the proportion of all Americans that believe President Bush is doing a good job is 42%, you then conduct a series of 10 polls to confirm or refute this claim of 42%. Describe your results if…

a) There is high bias and high variability in your results.
b) There is high bias and low variability in your results.
c) There is low bias and high variability in your results.
d) There is low bias and low variability in your results.

Answer 1

@Hero @phi

Answer 2

@phi ?

Answer 3

Your survey will give you a percent who say good job and a percent who say bad job.
you can find the average of the answers. If there is low bias, the average will be close to 42%. if there is high bias, the average will be far higher than 42% (or far lower)

variability will be difference between the averages of the 10 polls. If all 10 give roughly the same answer, you have low variability. Notice you could get 10 polls that each say 60%good job. that would be biased (far from 42%) , but low variability (all 10 give about the same answer)

Answer 4

a) There is high bias and high variability in your results.

Answer 5

what would i put for that?

Answer 6

@phi

Answer 7

if there is high bias, the average will be far higher than 42% (or far lower)

Answer 8

but what about with high versus low variability:? @phi

Answer 9

variability will be difference between the averages of the 10 polls. If all 10 give roughly the same answer, you have low variability.

Answer 10

im not sure how i would answer a tho?

Answer 11

Bias is related to skewedness, and variability is related to standard deviation.

Answer 12

if you write down 10 numbers and they are all wildly different from 42, you have high bias and high variability

Answer 13

Okay i get that. what about high bias, low variability

Answer 14

is this right for A?(a) If there is high bias and high variability, the numbers will not be anywhere near the 42 percent.
:

Answer 15

@phi

Answer 16

@amistre64

Answer 17

yes, give an example of 10 numbers

Answer 18

Ok what about b, c and d

Answer 19

phi seems to have a better handle on this then I would :)

Answer 20

k. What is high bias and low variabiliity ? @phi

Answer 21

High skewedness, and low standard deviation.

Answer 22

I dont thihnk thats what the question wants.. @phi are u stilll here

Answer 23

What is high bias and low variabiliity ?

what does high bias mean ?

low variability means all 10 polls give close to the same answer.

Answer 24

So would (b) be: The polls will be around 42.

Answer 25

no, around 42 is low bias

Answer 26

then im confused on high bias with low variability??

Answer 27

first, answer what does high bias mean ?

Answer 28

idk, alot of bias?

Answer 29

if there is high bias, the average will be far higher than 42% (or far lower)

Answer 30

ok but what about that AND low variability

Answer 31

you have 10 polls. each has an average. if they have high bias, the average is far from 42%.

variability is how much the answers differ from poll to poll. low variability means they all have close to the same average.

Answer 32

So (b) is: The average is far from 42 percent, with close to the same avergage.. that doesnt make sense

Answer 33

here is an example with 3 polls: 10%, 11%, 9%
they have almost the same average. but they are nowhere near 42%. they have high bias,
but low variability

Answer 34

can u explain to me how to word b please

Answer 35

lik ehow to word it.

Answer 36

I put If a certain number of polls have just about the same average, but are nowhere near 42 percent, they have high bias and low variability.

Answer 37

how about:
b) There is high bias and low variability in your results.

the poll results all are close to the same value, example: 20%, but far from 42%

Answer 38

what is low bias and low varibility

Answer 39

ok, c?

Answer 40

what do you think?

Answer 41

Umm. The average will be close to 42%?

Answer 42

all of the polls will be close to 42%,

Answer 43

So c is: All of the polls will be close to 42%?

Answer 44

yes

Answer 45

ok what baout d? im confused on that one

Answer 46

wait, that is for d)

Answer 47

oh ok, yeah
i mean what is c?

Answer 48

for
c) There is low bias and high variability in your results.

if you list the polls they will have a spread around 42%, and if you average the polls you will get 42%

low bias, high variablity might be 20% 82% 42% 74% 10%

Answer 49

If there is is low bias and high variability, if you list the polls they will have an average around 42 percent. If you average the polls, you'll get 42 percent low bias. The high variability might be 20, 72% 42% 63% 10%

Answer 50

is that right for c?

Answer 51

yes, but you should use your words, not mine

Answer 52

I will, but is this around right @phi ? (a) If there is high bias and high variability, the numbers will not be anywhere near the 42 percent value. If I wrote down 10 numbers and they were all completely different from 42, I would know that I have high bias and high variability.

(b) If a certain number of polls have just about the same average, but are nowhere near 42 percent, they have high bias and low variability. For example, 20 percent, but its far from 42 percent.

(c) If there is low bias and high variability, if you list the polls they will have an average around 42 percent. If you average the polls, you'll get 42 percent low bias. The high variability might be 20, 72% 42% 63% 10%

(d) If there is low bias and low variability, all of the polls will be close to 42 percent.