Self-Administered Reading Assessment
Statistical Reasoning
Question
1 -
1. Please identify the mean for the following distribution of numbers:
1, 4, 1, 2, 3, 2, 3, 2, 3, 2?
a. 2.0
b. 2.3
c. 2.5
d. 3.2
Question
2
2. Please
identify the median for the same distribution of numbers:
1, 4, 1, 2, 3, 2, 3, 2, 3, 2?
a. 2.0
b. 2.3
c. 2.5
d. 3.2
Question 3
3. In the following distribution of numbers, the mean
is _____ the mode and ______ the median: 4, 6, 1, 4, 5
a. less than; less than
b. less than; greater than
c. equal to; equal to
d. greater than; less than
Question 4
4. If scores on an exam have a mean of 50, a standard
deviation of 10, and are normally distributed, approximated 95 percent of those taking the
exam would be expected to score between:
a. 45 and 55
b. 40 and 60
c. 35 and 65
d. 30 and 70
Question 5
5. Jack's score on the psychology exam was the highest
in the class. What is his percentile rank for this score?
a. 99
b. 100
c. 95
d. The percentile rank can not be determined from the information
given.
Question 6
6. Please estimate the correlation coefficient for each
of the following scatterplots. Scatterplot A has a an correlation coefficient of ____;
Scatterplot B has a correlation coefficient of _____; Scatterplot C has a correlation of
______; Scatterplot D has a correlation of ______; and Scatterplot E has a correlation of
______.
a. r = +0.8; r = 0; r = -0.5; r = +1.0; r = -1.0
b. r = +0.8; r = -0.5; r = 0; r = -1.0; r = +1.0
c. r = +1.0; r = -1.0; r = +.0.8; r = -0.5; r = 0
d. r = -1.0; r = +1.0; r = -0.5; r = +0.8; r = 0
Question 7
7. If a distribution has a standard deviation of 0:
a. it must contain very few scores
b. it cannot be representative of the population from which it is
drawn
c. all of the scores in the distribution are equal
d. none of the above can be determined from the information given.
Question 8
8. The football team's punter wants to determine how
consistent her punting distances have been during the past season. She should compute the:
a. mean.
b. median.
c. mode.
d. standard deviation.
Question 9
9. Which statement about the following distributions is
true?
a. Distribution A has a larger
standard deviation and variance than distribution B
b. Distribution B has a larger standard deviation and variance than
distribution A
c. Distribution A has a larger standard deviation than distribution B
but a larger variance
d. Distribution B has a larger standard deviation than distribution A
but a larger variance
Self-Administered
Reading Assessment
Question 1
1. Please identify the mean
for the following distribution of numbers:
1, 4, 1, 2, 3, 2, 3, 2, 3, 2?
a. 2.0
Answer:
Sorry, not right. The mean is the sum of the scores divided by the number of scores. The sum of these 10 numbers is 23. To find the mean, you should divide 23 by 10.
Click here to return to question 1
Self-Administered
Reading Assessment
Question 1
1. Please identify the mean
for the following distribution of numbers:
1, 4, 1, 2, 3, 2, 3, 2, 3, 2?
b. 2.3
Answer:
This is correct. The mean is the sum of the scores divided by the number of scores. The sum of these 10 numbers is 23. To find the mean, you should divide 23 by 10.
Click here to return to question 1
Self-Administered
Reading Assessment
Question 1
1. Please identify the mean
for the following distribution of numbers:
1, 4, 1, 2, 3, 2, 3, 2, 3, 2?
c. 2.5
Answer:
Sorry, not right. The mean is the sum of the scores divided by the number of scores. The sum of these 10 numbers is 23. To find the mean, you should divide 23 by 10.
Click here to return to question 1
Self-Administered
Reading Assessment
Question 1
1. Please identify the mean
for the following distribution of numbers:
1, 4, 1, 2, 3, 2, 3, 2, 3, 2?
d. 3.2
Answer:
Sorry, not right. The mean is the sum of the scores divided by the number of scores. The sum of these 10 numbers is 23. To find the mean, you should divide 23 by 10.
Click here to return to question 1
Self-Administered
Reading Assessment
Question 2
2. Please
identify the median for the same distribution of numbers:
1, 4, 1, 2, 3, 2, 3, 2, 3, 2?
a.
2.0
Answer:
This is correct. When the
scores are put into order, 2 is at the 50th percentile, splitting the distribution in
half. The first step is to put the scores in order like this:
1, 1, 2, 2, 2, 2, 3, 3, 3, 4. Then, it is fairly simple to find the "middle
number".
Click here to return to question 2
Self-Administered
Reading Assessment
Question 2
2. Please
identify the median for the same distribution of numbers:
1, 4, 1, 2, 3, 2, 3, 2, 3, 2?
b.
2.3
Answer:
Sorry, not right. After placing the scores in order, look for the number that splits the
distribution in half. The first step is to put the scores in order like this:
1, 1, 2, 2, 2, 2, 3, 3, 3, 4. Then, it is fairly simple to find the "middle
number".
Click here to return to question 2
Self-Administered
Reading Assessment
Question 2
2. Please
identify the median for the same distribution of numbers:
1, 4, 1, 2, 3, 2, 3, 2, 3, 2?
c.
2.5
Answer:
Sorry, not right. After placing the scores in order, look for the number that splits the
distribution in half. The first step is to put the scores in order like this:
1, 1, 2, 2, 2, 2, 3, 3, 3, 4. Then, it is fairly simple to find the "middle
number".
Click here to return to question 2
Self-Administered
Reading Assessment
Question 2
2. Please
identify the median for the same distribution of numbers:
1, 4, 1, 2, 3, 2, 3, 2, 3, 2?
d.
3.2
Answer:
Sorry, not right. After placing the scores in order, look for the number that splits the
distribution in half. The first step is to put the scores in order like this:
1, 1, 2, 2, 2, 2, 3, 3, 3, 4. Then, it is fairly simple to find the "middle
number".
Click here to return to question 2
Self-Administered
Reading Assessment
Question 3
3. In the following distribution of numbers, the mean is
_____ the mode and ______ the median: 4, 6, 1, 4, 5
a. less
than; less than
Answer:
Sorry, not right. The first step in a problem like this is to calculate the mean, median, and mode.
To calculate the mean, simply add up each of the 5 values (they add up to 20), and divide the sum by 5. (20 divided by 5 is 4).
To calculate the median, simply arrange the numbers in order (like this: 1, 4, 4, 5, 6) and identify the number that splits the distribution in half (or you can think of it as the middle number). In this case the median is 4.
To calculate the mode, find which number occurs the most often (how many 1s are there? How many 4s are there? How many 5s? How many 6s?) Since there are more fours than any other number in this distribution, 4 is the mode.
To summarize the mean, median and mode all equal 4 for this distribution, they are all equal. (What does this tell you about whether this is a "normal" distribution?)
Click here to return to question 3
Self-Administered
Reading Assessment
Question 3
3. In the following distribution of numbers, the mean is
_____ the mode and ______ the median: 4, 6, 1, 4, 5
b.
less than; greater than
Answer:
Sorry, not right. The first step in a problem like this is to calculate the mean, median, and mode.
To calculate the mean, simply add up each of the 5 values (they add up to 20), and divide the sum by 5. (20 divided by 5 is 4).
To calculate the median, simply arrange the numbers in order (like this: 1, 4, 4, 5, 6) and identify the number that splits the distribution in half (or you can think of it as the middle number). In this case the median is 4.
To calculate the mode, find which number occurs the most often (how many 1s are there? How many 4s are there? How many 5s? How many 6s?) Since there are more fours than any other number in this distribution, 4 is the mode.
To summarize the mean, median and mode all equal 4 for this distribution, they are all equal. (What does this tell you about whether this is a "normal" distribution?)
Click here to return to question 3
Self-Administered
Reading Assessment
Question 3
3. In the following distribution of numbers, the mean is
_____ the mode and ______ the median: 4, 6, 1, 4, 5
c.
equal to; equal to
Answer:
This is correct. The first step in a problem like this is to calculate the mean, median, and mode.
To calculate the mean, simply add up each of the 5 values (they add up to 20), and divide the sum by 5. (20 divided by 5 is 4).
To calculate the median, simply arrange the numbers in order (like this: 1, 4, 4, 5, 6) and identify the number that splits the distribution in half (or you can think of it as the middle number). In this case the median is 4.
To calculate the mode, find which number occurs the most often (how many 1s are there? How many 4s are there? How many 5s? How many 6s?) Since there are more fours than any other number in this distribution, 4 is the mode.
To summarize the mean, median and mode all equal 4 for this distribution, they are all equal. (What does this tell you about whether this is a "normal" distribution?)
Click here to return to question 3
Self-Administered
Reading Assessment
Question 3
3. In the following distribution of numbers, the mean is
_____ the mode and ______ the median: 4, 6, 1, 4, 5
d.
greater than; less than
Answer:
Sorry, not right. The first step in a problem like this is to calculate the mean, median, and mode.
To calculate the mean, simply add up each of the 5 values (they add up to 20), and divide the sum by 5. (20 divided by 5 is 4).
To calculate the median, simply arrange the numbers in order (like this: 1, 4, 4, 5, 6) and identify the number that splits the distribution in half (or you can think of it as the middle number). In this case the median is 4.
To calculate the mode, find which number occurs the most often (how many 1s are there? How many 4s are there? How many 5s? How many 6s?) Since there are more fours than any other number in this distribution, 4 is the mode.
To summarize the mean, median and mode all equal 4 for this distribution, they are all equal. (What does this tell you about whether this is a "normal" distribution?)
Click here to return to question 3
Self-Administered
Reading Assessment
Question 4
4. If scores on an exam have a mean of 50, a
standard deviation of 10, and are normally distributed, approximated 95 percent of those
taking the exam would be expected to score between:
a. 45
and 55
Answer:
Sorry, not right. You need to increase your boundaries by 10 points for every standard deviation unit you want to include (because the standard deviation equals 10 points).The scores 45 and 55 are only 5 points above and below the mean. So, they would only include scores one half of one standard deviation above and below the mean.
To capture 95% of the scores in this particular distribution you would need to include 20 points above the mean (2 standard deviation units above the mean - each one is worth 10 points); and 20 points below the mean (2 standard deviation units below the mean - each one is worth 10 points).
The graphics below represent the scores associated with capturing 68% of the scores (one standard deviation above and below the mean); with capturing 95% of the scores (two standard deviations above and below the mean);and with capturing 99.7% of the scores (three standard deviations above and below the mean)
Click here to return to question 4
Self-Administered
Reading Assessment
Question 4
4. If scores on an exam have a mean of 50, a
standard deviation of 10, and are normally distributed, approximated 95 percent of those
taking the exam would be expected to score between:
b.
40 and 60
Answer:
Sorry, not right. You need to increase your boundaries by 10 points for every standard deviation unit you want to include (because the standard deviation equals 10 points).The scores 40 and 60 are exactly 10 points above and below the mean. So, they would only include scores one standard deviation above and below the mean. This would capture only 68% of the scores (not 95%).
To capture 95% of the scores in this particular distribution you would need to include 20 points above the mean (2 standard deviation units above the mean - each one is worth 10 points); and 20 points below the mean (2 standard deviation units below the mean - each one is worth 10 points).
The graphics below represent the scores associated with capturing 68% of the scores (one standard deviation above and below the mean); with capturing 95% of the scores (two standard deviations above and below the mean);and with capturing 99.7% of the scores (three standard deviations above and below the mean)
Click here to return to question 4
Self-Administered
Reading Assessment
Question 4
4. If scores on an exam have a mean of 50, a
standard deviation of 10, and are normally distributed, approximated 95 percent of those
taking the exam would be expected to score between:
c.
35 and 65
Answer:
Sorry, not right. You need to increase your boundaries by 10 points for every standard deviation unit you want to include (because the standard deviation equals 10 points).The scores 35 and 65 are 15 points above and below the mean. So, they would only include scores one and one half standard deviations above and below the mean. This would capture more than 68% of the scores but less than 95%.
To capture 95% of the scores in this particular distribution you would need to include 20 points above the mean (2 standard deviation units above the mean - each one is worth 10 points); and 20 points below the mean (2 standard deviation units below the mean - each one is worth 10 points).
The graphics below represent the scores associated with capturing 68% of the scores (one standard deviation above and below the mean); with capturing 95% of the scores (two standard deviations above and below the mean);and with capturing 99.7% of the scores (three standard deviations above and below the mean)
Click here to return to question 4
Self-Administered
Reading Assessment
Question 4
4. If scores on an exam have a mean of 50, a
standard deviation of 10, and are normally distributed, approximated 95 percent of those
taking the exam would be expected to score between:
d.
30 and 70
Answer:
This is correct. You need to increase your boundaries by 10 points for every standard deviation unit you want to include (because the standard deviation equals 10 points). The scores 30 and 70 are exactly 20 points above and below the mean. So, they would include scores two standard deviations above and below the mean. This would capture 95% of the scores .
To capture 95% of the scores in this particular distribution you would need to include 20 points above the mean (2 standard deviation units above the mean - each one is worth 10 points); and 20 points below the mean (2 standard deviation units below the mean - each one is worth 10 points).
The graphics below represent the scores associated with capturing 68% of the scores (one standard deviation above and below the mean); with capturing 95% of the scores (two standard deviations above and below the mean);and with capturing 99.7% of the scores (three standard deviations above and below the mean);
Click here to return to question 4
Self-Administered
Reading Assessment
Question 5
5. Jack's score on the psychology exam was the highest in
the class. What is his percentile rank for this score?
a. 99
Answer:
This is correct. A percentile rank of a score is the percentage of scores in a distribution that a given score exceeds. The highest score in the class exceeds 99 percent of the scores in the distribution - that is all of the scores except itself. It is not possible to have a percentile rank of 100. That would mean your score was higher than all of the scores in the distribution including yours . . . and of course, your score can't be higher than your own score.
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Self-Administered
Reading Assessment
Question 5
5. Jack's score on the psychology exam was the highest in
the class. What is his percentile rank for this score?
b.
100
Answer:
Sorry, not right. A percentile rank of a score is the percentage of scores in a distribution that a given score exceeds. The highest score in the class exceeds 99 percent of the scores in the distribution - that is all of the scores except itself. It is not possible to have a percentile rank of 100. That would mean your score was higher than all of the scores in the distribution including yours . . . and of course, your score can't be higher than your own score.
Click here to return to question 5
Self-Administered
Reading Assessment
Question 5
5. Jack's score on the psychology exam was the highest in
the class. What is his percentile rank for this score?
c. 95
Answer:
Sorry, not right. A percentile rank of a score is the percentage of scores in a distribution that a given score exceeds. The highest score in the class exceeds 99 percent of the scores in the distribution - that is all of the scores except itself. It is not possible to have a percentile rank of 100. That would mean your score was higher than all of the scores in the distribution including yours . . . and of course, your score can't be higher than your own score.
Click here to return to question 5
Self-Administered
Reading Assessment
Question 5
5. Jack's score on the psychology exam was the highest in
the class. What is his percentile rank for this score?
d.
The percentile rank can not be determined from the information given.
Answer:
Sorry, not right. A percentile rank of a score is the percentage of scores in a distribution that a given score exceeds. The highest score in the class exceeds 99 percent of the scores in the distribution - that is all of the scores except itself. It is not possible to have a percentile rank of 100. That would mean your score was higher than all of the scores in the distribution including yours . . . and of course, your score can't be higher than your own score.
Click here to return to question 5
Self-Administered
Reading Assessment
Question 6
6. Please estimate the correlation coefficient for each of
the following scatterplots. Scatterplot A has a an correlation coefficient of ____;
Scatterplot B has a correlation coefficient of _____; Scatterplot C has a correlation of
______; Scatterplot D has a correlation of ______; and Scatterplot E has a correlation of
______.
a. r
= +0.8; r = 0; r = -0.5; r = +1.0; r = -1.0
Answer:
Sorry, not right. Scatterplot A has a correlation coefficient of r = +1.0; Scatterplot B has a correlation coefficient of r = -1.0; Scatterplot C has a correlation of r = +0.8; Scatterplot D has a correlation of r = -0.5; and Scatterplot E has a correlation of r = 0.
An important point to this exercise is that by looking at the plots you can easily tell if the correlation is a positive or negative correlation (by which way the line slants); and you can tell if the correlation is a perfect 1.0 (by how perfectly the points fall on a straight line) or if it is not perfect and scatters a bit. Those are the only two things you need to know to be able to perfectly match up each of these scatterplots with the appropriate correlation coefficient. Is it a negative or positive slope, and are the points lined up with no scatter or are they scattered. Scatterplot E has no negative or positive slope and the points are widely scattered, so you can tell by these two things that there is no relationship between the two variables and the correlation coefficient equals zero.
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Self-Administered
Reading Assessment
Question 6
6. Please estimate the correlation coefficient for each of
the following scatterplots. Scatterplot A has a an correlation coefficient of ____;
Scatterplot B has a correlation coefficient of _____; Scatterplot C has a correlation of
______; Scatterplot D has a correlation of ______; and Scatterplot E has a correlation of
______.
b. r
= +0.8; r = -0.5; r = 0; r = -1.0; r = +1.0
Answer:
Sorry, not right. Scatterplot A has a correlation coefficient of r = +1.0; Scatterplot B has a correlation coefficient of r = -1.0; Scatterplot C has a correlation of r = +0.8; Scatterplot D has a correlation of r = -0.5; and Scatterplot E has a correlation of r = 0.
An important point to this exercise is that by looking at the plots you can easily tell if the correlation is a positive or negative correlation (by which way the line slants); and you can tell if the correlation is a perfect 1.0 (by how perfectly the points fall on a straight line) or if it is not perfect and scatters a bit. Those are the only two things you need to know to be able to perfectly match up each of these scatterplots with the appropriate correlation coefficient. Is it a negative or positive slope, and are the points lined up with no scatter or are they scattered. Scatterplot E has no negative or positive slope and the points are widely scattered, so you can tell by these two things that there is no relationship between the two variables and the correlation coefficient equals zero.
Click here to return to question 6
Self-Administered
Reading Assessment
Question 6
6. Please estimate the correlation coefficient for each of
the following scatterplots. Scatterplot A has a an correlation coefficient of ____;
Scatterplot B has a correlation coefficient of _____; Scatterplot C has a correlation of
______; Scatterplot D has a correlation of ______; and Scatterplot E has a correlation of
______.
c. r
= +1.0; r = -1.0; r = +.0.8; r = -0.5; r = 0
Answer:
This is correct. Scatterplot A has a correlation coefficient of r = +1.0; Scatterplot B has a correlation coefficient of r = -1.0; Scatterplot C has a correlation of r = +0.8; Scatterplot D has a correlation of r = -0.5; and Scatterplot E has a correlation of r = 0.
An important point to this exercise is that by looking at the plots you can easily tell if the correlation is a positive or negative correlation (by which way the line slants); and you can tell if the correlation is a perfect 1.0 (by how perfectly the points fall on a straight line) or if it is not perfect and scatters a bit. Those are the only two things you need to know to be able to perfectly match up each of these scatterplots with the appropriate correlation coefficient. Is it a negative or positive slope, and are the points lined up with no scatter or are they scattered. Scatterplot E has no negative or positive slope and the points are widely scattered, so you can tell by these two things that there is no relationship between the two variables and the correlation coefficient equals zero.
Click here to return to question 6
Self-Administered
Reading Assessment
Question 6
6. Please estimate the correlation coefficient for each of
the following scatterplots. Scatterplot A has a an correlation coefficient of ____;
Scatterplot B has a correlation coefficient of _____; Scatterplot C has a correlation of
______; Scatterplot D has a correlation of ______; and Scatterplot E has a correlation of
______.
d. r
= -1.0; r = +1.0; r = -0.5; r = +0.8; r = 0
Answer:
Sorry, not right. Scatterplot A has a correlation coefficient of r = +1.0; Scatterplot B has a correlation coefficient of r = -1.0; Scatterplot C has a correlation of r = +0.8; Scatterplot D has a correlation of r = -0.5; and Scatterplot E has a correlation of r = 0.
An important point to this exercise is that by looking at the plots you can easily tell if the correlation is a positive or negative correlation (by which way the line slants); and you can tell if the correlation is a perfect 1.0 (by how perfectly the points fall on a straight line) or if it is not perfect and scatters a bit. Those are the only two things you need to know to be able to perfectly match up each of these scatterplots with the appropriate correlation coefficient. Is it a negative or positive slope, and are the points lined up with no scatter or are they scattered. Scatterplot E has no negative or positive slope and the points are widely scattered, so you can tell by these two things that there is no relationship between the two variables and the correlation coefficient equals zero.
Click here to return to question 6
Self-Administered
Reading Assessment
Question 7
7. If a distribution has a standard deviation
of 0:
a.
it must contain very few scores
Answer:
Sorry, this is not correct. Whether a distribution has many scores or only a few scores does not determine whether or not the standard deviation is zero. A small distribution of only 2 or 3 scores can have a large standard deviation, while a huge distribution of many thousands can have a standard deviation of zero - if all of the scores are the same score. For example, if you were to test all of the second graders in the country to see what grade they were in (which would be a bit silly), but you would find that they were all in second grade. They would all have the same score, and a standard deviation of zero.
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Self-Administered
Reading Assessment
Question 7
7. If a distribution has a standard deviation
of 0:
b.
it cannot be representative of the population from which it is drawn
Answer:
Sorry, this is not correct. A distribution that has a standard deviation of 0, may be representative of the population from which it is drawn if that population also has a standard deviation of zero. A population can have a standard deviation of zero - if all of the scores are the same score. For example, if you were to test all of the second graders in the country to see what grade they were in (which would be a bit silly), but you would find that they were all in second grade. They would all have the same score, and a standard deviation of zero. This is true if you test the whole population, or just a sample of that population.
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Self-Administered
Reading Assessment
Question 7
7. If a distribution has a standard deviation
of 0:
c.
all of the scores in the distribution are equal
Answer:
This is correct. A distribution can have a standard deviation of zero - if all of the scores are the same score. For example, if you were to test all of the second graders in the country to see what grade they were in (which would be a bit silly), but you would find that they were all in second grade. They would all have the same score, and a standard deviation of zero.
Click here to return to question 7
Self-Administered
Reading Assessment
Question 7
7. If a distribution has a standard deviation
of 0:
d.
none of the above can be determined from the information given.
Answer:
Sorry, this is not correct. A distribution can have a standard deviation of zero - if all of the scores are the same score. For example, if you were to test all of the second graders in the country to see what grade they were in (which would be a bit silly), but you would find that they were all in second grade. They would all have the same score, and a standard deviation of zero.
Click here to return to question 7
Self-Administered
Reading Assessment
Question 8
8. The football team's punter wants to
determine how consistent her punting distances have been during the past season. She
should compute the:
a. mean.
Answer:
Sorry, this is not correct. The mean would tell her on average how far she punted, but would not give any indication of how consistent she was.
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Self-Administered
Reading Assessment
Question 8
8. The football team's punter wants to
determine how consistent her punting distances have been during the past season. She
should compute the:
b.
median.
Answer:
Sorry, this is not correct. The median would tell her the middle score, once she ordered her punting distances from shortest to farthest. It would not, however give any indication of how consistent she was.
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Self-Administered
Reading Assessment
Question 8
8. The football team's punter wants to
determine how consistent his punting distances have been during the past season. She
should compute the:
c.
mode.
Answer:
Sorry, this is not correct. The mode would tell her which distance she kicks most frequently, but would not give any indication of how consistent she was.
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Self-Administered
Reading Assessment
Question 8
8. The football team's punter wants to
determine how consistent his punting distances have been during the past season. She
should compute the:
d.
standard deviation.
Answer:
This is correct. The standard deviation would provide an indication of how consistent she was. Do the distances of the punt vary widely or does she tend to kick about the same distance every time.
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Self-Administered
Reading Assessment
Question 9
9. Which statement about the following
distributions is true?
a. Distribution
A has a larger standard deviation and variance than distribution B
Answer:
This is correct. Distribution A looks more spread out. There are some very high scores and some very low scores, and lots in between. Distribution B, however, looks much more narrow. It appears to have very few high or low scores, they all seem to be clustering right around the mean.
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Self-Administered
Reading Assessment
Question 9
9. Which statement about the following distributions is
true?
b.
Distribution B has a larger standard deviation and variance than distribution A
Answer:
Sorry, this is not correct. Distribution A looks more spread out than Distribution B. There are some very high scores and some very low scores, and lots in between. Consequently, Distribution A will have a larger standard deviation and variance. Distribution B, however, looks much more narrow. It appears to have very few high or low scores, they all seem to be clustering right around the mean. This gives Distribution B a smaller standard deviation and variance.
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Self-Administered
Reading Assessment
Question 9
9. Which statement about the following distributions is
true?
c.
Distribution A has a larger standard deviation than distribution B but a larger variance
Answer:
Sorry, this is not correct. While it is true that Distribution A has a larger standard deviation than B, it is also true that it has a larger variance. These two concepts are very closely linked (the standard deviation is simply the square root of the variance), so that if one distribution is has a larger variance it must have a larger standard deviation.
Distribution A looks more spread out than Distribution B. There are some very high scores and some very low scores, and lots in between. Consequently, Distribution A will have a larger standard deviation and variance. Distribution B, however, looks much more narrow. It appears to have very few high or low scores, they all seem to be clustering right around the mean. This gives Distribution B a smaller standard deviation and variance.
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Self-Administered
Reading Assessment
Question 9
9. Which statement about the following distributions is
true?
d.
Distribution B has a larger standard deviation than distribution A but a larger variance
Answer:
Sorry, this is not correct. Distribution A looks more spread out than Distribution B. There are some very high scores and some very low scores, and lots in between. Consequently, Distribution A will have a larger standard deviation and variance. Distribution B, however, looks much more narrow. It appears to have very few high or low scores, they all seem to be clustering right around the mean. This gives Distribution B a smaller standard deviation and variance.
These two concepts (standard deviation & variance) are very closely linked (the standard deviation is simply the square root of the variance), so that if one distribution is has a larger variance it must have a larger standard deviation.
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