STATS 244.3(01)
Elementary Statistical Concepts
Term Test #1 , September 24, 1998
© 1998 by Mikelis Bickis

The answer is (g) 10.
(11+5+11+6+11+6)/6=10
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The answer is (h) 11.
If we put the numbers in order we get
5 6 11 11 11 16
Since there are 6 numbers, and (6+1)/2=3.5, the median is between the
third and fourth numbers. Since these are both 11, the median is 11.
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The answer is (h) 11.
This is the number occurring the most frequently. 11 appears 3 times, the other numbers
only appear once each.
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The answer is (i) 16.
The deviations and their squares are
1110 = 1 and 1² = 1
510 = 5 and (5)² = 25
1110 = 1 and 1² = 1
610 = 4 and (4)² = 16
1110 = 1 and 1² = 1
1610 = 6 and 6² = 36
The sum of the squared deviations add up to 80. For the sample variance
we divide by 61=5, and 80/5=16.
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The answer is (b) 4.
The standard deviation is the square root of the variance, and
4²=16.
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The answer is (d) 6.
Putting the numbers in order gives
5 6 11 11 11 16.
The numbers to the left of the median are
5 6 11
and the median of these is 6.
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The answer is (h) 11.
Putting the numbers in order gives
5 6 11 11 11 16.
The numbers to the right of the median are
11 11 16
and the median of these is 11
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.

The answer is (c) 5.
The lower quartile is 6, and the upper quartile is 11, so the interquartile
range is 116=5.
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The answer is (h) 11.
The largest number is 16, the smallest is 5. The difference is 165=11.
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The answer is (h) 11.
The 75th percentile is the same as the upper quartile.
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An attribute of an individual (or "unit") is called a variable.
Nonnumeric variables are called categorical. So the answer is
(i) categorical variable
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The answer is (d) parameter. Remember Population Parameter.
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 (a) Sample. A subset of the population is called a sample.
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 (f) Outlier.
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 Mean squared deviation from the mean is the verbal definition
of the (c) variance.
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Wrong. It is not a histograma histogram has bars.
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Correct. This is an example of a stemplot or stemandleaf diagram.
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Wrong. A cumulative distribution would be a line graph.
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Wrong. No box, no whiskers.
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Wrong. We haven't even discussed scatterplots in this course yet. This
choice is put there to catch smartalecks who figure they must have
missed something.
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Not 7.
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Not 14.
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Correct. Each leaf represents an observation ("unit"), and one
can count that there are 15 leaves.
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Not 53.
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Not 77.
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Wrong. There is no 11. Only single digits appear in the leaves.
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Wrong. Why would you think 13?
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Not quite. The smallest first digit is 8, but the diagram has more.
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Correct. The smallest first digit is 8, and the smallest second digit
is 1. Actually, one cannot tell from the stemplot
where the decimal point is, but the choices from the following questions
make clear where it must be.
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Could be correct. The smallest number could be 811, since the first two
digits are still 8 and 1, respectively. However, this choice is not
consistent with any of the values from the remaining questions.
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Not 96. There are 6 smaller observations, and 8 larger.
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Correct.There are 7 smaller observations, and 7 larger.
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Not 99. There are 8 smaller observations, and 6 larger.
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Wrong. There is no 110.
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Not even close. There are 11 smaller observations, and only 3 larger.
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The answer is (c) 33. The quartiles would be the 4th observations from
either end, thus the lower quartile is 82, and the upper is 115. The
interquartile range is the difference of these.
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Wrong. This is a stemplot for some other data.
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Wrong. The median and the quartiles are in the wrong places.
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Correct. Note that median and quartiles are in the correct places.
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Wrong. The shape is correct, but note that the numbers along the
abcissa do not agree with the values in the stemplot.
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Not even close. This looks like a cumulative distribution, but most of
the values are greater than 10.
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It is not symmetrical, and there don't appear to be outliers.
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It is not symmetrical.
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Correct. The distribution is positively skewed
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It is not negatively skewed.
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Wrong. To have a variance of zero, all the values would have to be the same.
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Wrong. This histogram would not balance at 10.
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Wrong. It would not balance at 20 either
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Wrong. This is the "centre" of the distribution in one sense  in fact
it is like the mode, but there is more weight to the right than to the
left, so again it would not balance.
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Not quite. The median is around 30. But for a skewed distribution like
this one, the mean and median are not usually equal. On the other hand,
the histogram does not tell you exactly where the values are. If all
the values were pushed to the left side of the intervals (as they
could be, if the left endpoints are included), then it is possible for
the median to be less than 30  in fact, the median could be as low
as 25. Thus, one could argue that a distribution
having a mean around 30 is not inconsistent with this
histogram. Hence, I will give full marks to those who selected this choice.
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Correct. The mean would be to the right of the median, so it
would be somewhat greater than 30. If you suppose that the values are
concentrated at the midpoints of the intervals, you can figure out that
the mean would be 33. Since one could argue that 33
is `around 30' the previous choice is also acceptable.
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20% of the values are less than 20, and 20+30=50% are less than 30, so
the 25th percentile is somewhere between these values. Thus the correct
answer is (b) between 20 and 30.
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All the bars except the last one represent values less than 60. The
last bar comprises 5%, so the remaining ones make up 95%. Thus the
answer is (d).
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