Thread: statistics help

16, 21, 21, 22, 22, 23, 24, 24, 25, 25, 25, 25, 26, 26, 26, 26, 27, 27, 28, 20, 29, 29, 31, 32, 33, 33, 35, 35, 36, 37

This data is the ages of mothers.

The ages in the sample have presumably been rounded down since eg a mother aged 27 3/4 would have given her age as 27. What effect will this have on your estimate of the mean and standard deviation? Suggest possible corrections to the estimates, distinguishing clearly between the corrected and the uncorrected value.

Originally Posted by princess_anna57

16, 21, 21, 22, 22, 23, 24, 24, 25, 25, 25, 25, 26, 26, 26, 26, 27, 27, 28, 20, 29, 29, 31, 32, 33, 33, 35, 35, 36, 37

This data is the ages of mothers.

The ages in the sample have presumably been rounded down since eg a mother aged 27 3/4 would have given her age as 27. What effect will this have on your estimate of the mean and standard deviation? Suggest possible corrections to the estimates, distinguishing clearly between the corrected and the uncorrected value.

The mean will be biased down by 0.5 years. So a corrected mean would be Sample_Mean+0.5


RonL

Originally Posted by princess_anna57

16, 21, 21, 22, 22, 23, 24, 24, 25, 25, 25, 25, 26, 26, 26, 26, 27, 27, 28, 20, 29, 29, 31, 32, 33, 33, 35, 35, 36, 37

This data is the ages of mothers.

The ages in the sample have presumably been rounded down since eg a mother aged 27 3/4 would have given her age as 27. What effect will this have on your estimate of the mean and standard deviation? Suggest possible corrections to the estimates, distinguishing clearly between the corrected and the uncorrected value.

As the Rv is the sum of the two RV's Reported Age and an error epsilon:

TrueAge=ReportedAge+epsilon

Now assume Reported Age and epsilon are independent (they are not necessarily but will
be near enough for our purposes), then:

var(TrueAge)=var(ReportedAge) + var(epsilon)

Now epsilon ~U(0,1), so var(epsilon)=1/12. So:

SD(TrueAge)=sqrt(SD(ReportedAge)^2 + 1/12)

RonL