# STATS 244.3(01) Elementary Statistical Concepts

## Term Test #1 , September 24, 1998

1. The answer is (g) 10.

(11+5+11+6+11+6)/6=10

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3. 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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4. 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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5. The answer is (i) 16.

The deviations and their squares are

11-10 = 1 and 1² = 1
5-10 = -5 and (-5)² = 25
11-10 = 1 and 1² = 1
6-10 = -4 and (-4)² = 16
11-10 = 1 and 1² = 1
16-10 = 6 and 6² = 36

The sum of the squared deviations add up to 80. For the sample variance we divide by 6-1=5, and 80/5=16.

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6. The answer is (b) 4.

The standard deviation is the square root of the variance, and 4²=16.

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7. 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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8. 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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9. The answer is (c) 5.

The lower quartile is 6, and the upper quartile is 11, so the inter-quartile range is 11-6=5.

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10. The answer is (h) 11.

The largest number is 16, the smallest is 5. The difference is 16-5=11.

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11. The answer is (h) 11.

The 75th percentile is the same as the upper quartile.

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12. An attribute of an individual (or "unit") is called a variable. Non-numeric variables are called categorical. So the answer is (i) categorical variable

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13. The answer is (d) parameter. Remember Population Parameter.

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14. (a) Sample. A subset of the population is called a sample.

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15. (f) Outlier.

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16. Mean squared deviation from the mean is the verbal definition of the (c) variance.

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1. Wrong. It is not a histogram--a histogram has bars.

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2. Correct. This is an example of a stemplot or stem-and-leaf diagram.

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3. Wrong. A cumulative distribution would be a line graph.

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4. Wrong. No box, no whiskers.

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5. Wrong. We haven't even discussed scatterplots in this course yet. This choice is put there to catch smart-alecks who figure they must have missed something.

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1. Not 7.

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2. Not 14.

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3. Correct. Each leaf represents an observation ("unit"), and one can count that there are 15 leaves.

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4. Not 53.

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5. Not 77.

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1. Wrong. There is no 11. Only single digits appear in the leaves.

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2. Wrong. Why would you think 13?

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3. Not quite. The smallest first digit is 8, but the diagram has more.

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4. 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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5. 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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1. Not 96. There are 6 smaller observations, and 8 larger.

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2. Correct.There are 7 smaller observations, and 7 larger.

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3. Not 99. There are 8 smaller observations, and 6 larger.

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4. Wrong. There is no 110.

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5. Not even close. There are 11 smaller observations, and only 3 larger.

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17. 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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1. Wrong. This is a stemplot for some other data.

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2. Wrong. The median and the quartiles are in the wrong places.

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3. Correct. Note that median and quartiles are in the correct places.

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4. 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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5. Not even close. This looks like a cumulative distribution, but most of the values are greater than 10.

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1. It is not symmetrical, and there don't appear to be outliers.

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2. It is not symmetrical.

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3. Correct. The distribution is positively skewed

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4. It is not negatively skewed.

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5. Wrong. To have a variance of zero, all the values would have to be the same.

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1. Wrong. This histogram would not balance at 10.

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2. Wrong. It would not balance at 20 either

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3. 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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4. 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 end-points 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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5. 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 mid-points 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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18. 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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19. 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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