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Part I
Exploring and Understanding Data
Review of Part I – Exploring and Understanding Data
1. Bananas.
a)
A histogram of the prices of bananas from 15
markets, as reported by the USDA, appears
at the right.
b)
The distribution of banana prices is skewed
to the left, so median and IQR are
appropriate measures of center and spread.
Median = 49 cents per pound
IQR = 7 cents per pound
c)
The distribution of the prices of bananas
from 15 markets, as reported by the USDA, is
unimodal and skewed to the left.
The center
of the distribution is approximately 50 cents, with the lowest price 42 cents per pound and
the highest price 53 cents per pound.
2. Prenatal care.
a)
54 39 61
3
513
...
.
++
=
,
so the overall rate of 5.1 deaths per thousand live births is equal to the
average of the rates for Intensive, Adequate, and Inadequate prenatal care, when rounded
to the nearest tenth.
There is no reason this should be the case unless the number of
women receiving each type of prenatal care is approximately the same.
b)
Yes, the results indicate (but do not prove) that adequate prenatal care is important for
pregnant women. The mortality rate is quite a bit lower for women with adequate care
than for other women.
c)
No, the results do not suggest that a woman pregnant with twins should be wary of
seeking too much medical care. Intensive care is given for emergency conditions.
The data
do not
suggest that the level of care is the cause of the higher mortality.
3. Singers.
a)
The two statistics could be the same if there were many sopranos of that height.
b)
The distribution of heights of each voice part is roughly symmetric. The basses and tenors
are generally taller than the altos and sopranos, with the basses being slightly taller than
the tenors. The sopranos and altos have about the same median height. Heights of basses
and sopranos are more consistent than altos and tenors.
4. Dialysis.
There are only three patients currently on dialysis.
With so few patients, no display is
needed.
We know that one patient has had his or her toes amputated and that two patients
have developed blindness.
What we don’t know is whether or not the patient that has had
his or her toes amputated has also developed blindness.
Even if we wanted to, we do not
have enough information to make an appropriate display.
42
46
50
54
1
2
3
4
Banana Prices
Price (cents per pound)
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81
5. Beanstalks.
a)
The greater standard deviation for the distribution of women’s heights means that their
heights are more variable than the heights of men.
b)
The zscore for women to qualify is 2.4 compared with 1.75 for men, so it is harder for men
to qualify.
6. Bread.
a)
The distribution of the number of loaves sold each day in the last 100 days at the
Clarksburg Bakery is unimodal and skewed to the right.
The mode is near 100, with the
majority of days recording fewer than 120 loaves sold.
The number of loaves sold ranges
from 95 to 140.
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 Spring '08
 WEINSTEIN
 Normal Distribution, Standard Deviation, normal model

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