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Describing Distributions with
Numbers
BPS chapter 2
© 2010 W.H. Freeman and Company
1. Median
1. Find the median of the following 9 numbers:
43 54 55 63 67 68 69 77 85
a)
b)
c)
d)
65
64
67
64.6
1. Median (answer)
Find the median of the following 9 numbers:
43 54 55 63 67 68 69 77 85
a)
b)
c)
d)
65
64
67
64.6
2. Median
For the data in the previous question,
43 54 55 63 67 68 69 77 85
Suppose that the last data point is actually 115 instead of 85. What
effect would this new maximum have on our value for the median of
the dataset?
a)
b)
c)
Increase the value of the median.
Decrease the value of the median.
Not change the value of the median.
2. Median (answer)
For the data in the previous question,
43 54 55 63 67 68 69 77 85
Suppose that the last data point is actually 115 instead of 85. What
effect would this new maximum have on our value for the median of
the dataset?
a)
b)
c)
Increase the value of the median.
Decrease the value of the median.
Not change the value of the median.
3. Mean
For the data in the previous question,
43 54 55 63 67 68 69 77 85
Suppose that the last data point is actually 115 instead of 85. What
effect would this new maximum have on our value for the mean of
the dataset?
a)
b)
c)
Increase the value of the mean.
Decrease the value of the mean.
Not change the value of the mean.
3. Mean (answer)
For the data in the previous question,
43 54 55 63 67 68 69 77 85
Suppose that the last data point is actually 115 instead of 85. What
effect would this new maximum have on our value for the mean of
the dataset?
a)
b)
c)
Increase the value of the mean.
Decrease the value of the mean.
Not change the value of the mean.
4. Mean vs. median
For the dataset “sales prices of homes in Los Angeles,” should you use
the mean or the median to describe the center?
a)
b)
Mean
Median
4. Mean vs. median (answer)
For the dataset “sales prices of homes in Los Angeles,” should you use
the mean or the median to describe the center?
a)
b)
Mean
Median
5. Mean vs. median
For the dataset “incomes for people in the United States,” should you
use the mean or the median to describe the center?
a)
b)
Mean
Median
5. Mean vs. median (answer)
For the dataset “incomes for people in the United States,” should you
use the mean or the median to describe the center?
a)
b)
Mean
Median
6. Comparing two histograms
Compare the centers of Distribution A (Female Shoulder Girth) and
Distribution B (Male Shoulder Girth) shown below.
a)
b)
c)
The center of Distribution A is greater than the center of Distribution
B.
The center of Distribution A is less than the center of Distribution B.
The center of Distribution A is equal to the center of Distribution B.
6. Comparing two histograms (answer)
Compare the centers of Distribution A (Female Shoulder Girth) and
Distribution B (Male Shoulder Girth) shown below.
a)
b)
c)
The center of Distribution A is greater than the center of Distribution
B.
The center of Distribution A is less than the center of
Distribution B.
The center of Distribution A is equal to the center of Distribution B.
7. In the data below Ashley has a Z
score of .29. That means:
A.
B.
C.
D.
E.
She is above
average
She is 29%
above average
She is 29 inches
above average
She is 29 dollars
richer than the
average
All of the above
Student
Flowr% deviation sq.deviationz score
Baldwin, David C
30%
-23%
5.49%
-1.05
Smith, Lindsay Eliza
30%
-23%
5.49%
-1.05
Watson, Jacqueline
30%
-23%
5.49%
-1.05
Cardona, Camille Tai
40%
-13%
1.81%
-0.60
Carter, Hayley Noell
40%
-13%
1.81%
-0.60
Lazarus, Le'ondra He
40%
-13%
1.81%
-0.60
Scott, Shannon Lasha 40%
-13%
1.81%
-0.60
Hendrix, Amber Nicol 45%
-8%
0.71%
-0.38
Radke, Carrie Nicole
50%
-3%
0.12%
-0.15
Richardson, Jordan R 50%
-3%
0.12%
-0.15
Dew, Dougie Brendan 60%
7%
0.43%
0.29
Persohn, Ashley Dani 60%
7%
0.43%
0.29
Harber, Hannah Taylo 70%
17%
2.74%
0.74
Roberson, Jasmine Mi 70%
17%
2.74%
0.74
Smith, Lindsay Nicol 100%
47%
21.68%
2.09
Wise, Alisha
100%
47%
21.68%
2.09
7. In the data below Ashley has a Z
score of .29. That means:
A.
B.
C.
D.
E.
She is above
average
She is 29%
above average
She is 29 inches
above average
She is 29 dollars
richer than the
average
All of the above
Student
Flowr% deviation sq.deviationz score
Baldwin, David C
30%
-23%
5.49%
-1.05
Smith, Lindsay Eliza
30%
-23%
5.49%
-1.05
Watson, Jacqueline
30%
-23%
5.49%
-1.05
Cardona, Camille Tai
40%
-13%
1.81%
-0.60
Carter, Hayley Noell
40%
-13%
1.81%
-0.60
Lazarus, Le'ondra He
40%
-13%
1.81%
-0.60
Scott, Shannon Lasha 40%
-13%
1.81%
-0.60
Hendrix, Amber Nicol 45%
-8%
0.71%
-0.38
Radke, Carrie Nicole
50%
-3%
0.12%
-0.15
Richardson, Jordan R 50%
-3%
0.12%
-0.15
Dew, Dougie Brendan 60%
7%
0.43%
0.29
Persohn, Ashley Dani 60%
7%
0.43%
0.29
Harber, Hannah Taylo 70%
17%
2.74%
0.74
Roberson, Jasmine Mi 70%
17%
2.74%
0.74
Smith, Lindsay Nicol 100%
47%
21.68%
2.09
Wise, Alisha
100%
47%
21.68%
2.09
8. Which of the following tells us about
the group?
A.
B.
C.
D.
E.
The raw score
The Z score
The deviation
score
The mean
All of the above
Student
Flowr% deviation sq.deviationz score
Baldwin, David C
30%
-23%
5.49%
-1.05
Smith, Lindsay Eliza
30%
-23%
5.49%
-1.05
Watson, Jacqueline
30%
-23%
5.49%
-1.05
Cardona, Camille Tai
40%
-13%
1.81%
-0.60
Carter, Hayley Noell
40%
-13%
1.81%
-0.60
Lazarus, Le'ondra He
40%
-13%
1.81%
-0.60
Scott, Shannon Lasha 40%
-13%
1.81%
-0.60
Hendrix, Amber Nicol 45%
-8%
0.71%
-0.38
Radke, Carrie Nicole
50%
-3%
0.12%
-0.15
Richardson, Jordan R 50%
-3%
0.12%
-0.15
Dew, Dougie Brendan 60%
7%
0.43%
0.29
Persohn, Ashley Dani 60%
7%
0.43%
0.29
Harber, Hannah Taylo 70%
17%
2.74%
0.74
Roberson, Jasmine Mi 70%
17%
2.74%
0.74
Smith, Lindsay Nicol 100%
47%
21.68%
2.09
Wise, Alisha
100%
47%
21.68%
2.09
8. Which of the following tells us about
the group?
A.
B.
C.
D.
E.
The raw score
The Z score
The deviation
score
The mean
All of the above
Student
Flowr% deviation sq.deviationz score
Baldwin, David C
30%
-23%
5.49%
-1.05
Smith, Lindsay Eliza
30%
-23%
5.49%
-1.05
Watson, Jacqueline
30%
-23%
5.49%
-1.05
Cardona, Camille Tai
40%
-13%
1.81%
-0.60
Carter, Hayley Noell
40%
-13%
1.81%
-0.60
Lazarus, Le'ondra He
40%
-13%
1.81%
-0.60
Scott, Shannon Lasha 40%
-13%
1.81%
-0.60
Hendrix, Amber Nicol 45%
-8%
0.71%
-0.38
Radke, Carrie Nicole
50%
-3%
0.12%
-0.15
Richardson, Jordan R 50%
-3%
0.12%
-0.15
Dew, Dougie Brendan 60%
7%
0.43%
0.29
Persohn, Ashley Dani 60%
7%
0.43%
0.29
Harber, Hannah Taylo 70%
17%
2.74%
0.74
Roberson, Jasmine Mi 70%
17%
2.74%
0.74
Smith, Lindsay Nicol 100%
47%
21.68%
2.09
Wise, Alisha
100%
47%
21.68%
2.09
8. Standard deviation
Which of the following statements is TRUE?
a)
b)
c)
d)
Standard deviation has no unit of measurement.
Standard deviation is either positive or negative.
Standard deviation is inflated by outliers.
Standard deviation is used even when the mean is not an
appropriate measure of center.
8. Standard deviation (answer)
Which of the following statements is TRUE?
a)
b)
c)
d)
Standard deviation has no unit of measurement.
Standard deviation is either positive or negative.
Standard deviation is inflated by outliers.
Standard deviation is used even when the mean is not an
appropriate measure of center.
9. Center and spread
For the following distribution of major league baseball players’ salaries
in 1992, which measures of center and spread are more
appropriate?
a)
b)
Mean and standard deviation
Median and interquartile range
Center and spread (answer)
For the following distribution of major league baseball players’ salaries
in 1992, which measures of center and spread are more
appropriate?
a)
b)
Mean and standard deviation
Median and interquartile range
10. Center and spread
Which measure uses all the data?
a)
b)
c)
d)
e)
Mean
standard deviation
Median
Mode
A and B
10. Center and spread
Which measure uses all the data?
a)
b)
c)
d)
e)
Mean
standard deviation
Median
Mode
A and B
11. Which of the following tells us about
the individual?
A.
B.
C.
D.
E.
The raw score
The Z score
The deviation
score
The percent
correct
All of the above
Student
Flowr% deviation sq.deviationz score
Baldwin, David C
30%
-23%
5.49%
-1.05
Smith, Lindsay Eliza
30%
-23%
5.49%
-1.05
Watson, Jacqueline
30%
-23%
5.49%
-1.05
Cardona, Camille Tai
40%
-13%
1.81%
-0.60
Carter, Hayley Noell
40%
-13%
1.81%
-0.60
Lazarus, Le'ondra He
40%
-13%
1.81%
-0.60
Scott, Shannon Lasha 40%
-13%
1.81%
-0.60
Hendrix, Amber Nicol 45%
-8%
0.71%
-0.38
Radke, Carrie Nicole
50%
-3%
0.12%
-0.15
Richardson, Jordan R 50%
-3%
0.12%
-0.15
Dew, Dougie Brendan 60%
7%
0.43%
0.29
Persohn, Ashley Dani 60%
7%
0.43%
0.29
Harber, Hannah Taylo 70%
17%
2.74%
0.74
Roberson, Jasmine Mi 70%
17%
2.74%
0.74
Smith, Lindsay Nicol 100%
47%
21.68%
2.09
Wise, Alisha
100%
47%
21.68%
2.09
11. Which of the following tells us about
the individual?
A.
B.
C.
D.
E.
The raw score
The Z score
The deviation
score
The percent
correct
All of the
above
Student
Flowr% deviation sq.deviationz score
Baldwin, David C
30%
-23%
5.49%
-1.05
Smith, Lindsay Eliza
30%
-23%
5.49%
-1.05
Watson, Jacqueline
30%
-23%
5.49%
-1.05
Cardona, Camille Tai
40%
-13%
1.81%
-0.60
Carter, Hayley Noell
40%
-13%
1.81%
-0.60
Lazarus, Le'ondra He
40%
-13%
1.81%
-0.60
Scott, Shannon Lasha 40%
-13%
1.81%
-0.60
Hendrix, Amber Nicol 45%
-8%
0.71%
-0.38
Radke, Carrie Nicole
50%
-3%
0.12%
-0.15
Richardson, Jordan R 50%
-3%
0.12%
-0.15
Dew, Dougie Brendan 60%
7%
0.43%
0.29
Persohn, Ashley Dani 60%
7%
0.43%
0.29
Harber, Hannah Taylo 70%
17%
2.74%
0.74
Roberson, Jasmine Mi 70%
17%
2.74%
0.74
Smith, Lindsay Nicol 100%
47%
21.68%
2.09
Wise, Alisha
100%
47%
21.68%
2.09
The End