LSP 121-405
In-Class Activity 5
Working with PASW
20 points
Due by Saturday, Oct. 17th 11:59 pm
ANSWERS
Statistics
Age at Inauguration
N
Valid
44
Missing
0
Mean
54.64
Median
54.50
Mode
54
Std. Deviation
6.273
Range
27
Minimum
42
Maximum
69
Percentiles
25
50.25
50
54.50
75
57.75
Age at Inauguration
Cumulative
Frequency
Valid
Percent
Valid Percent
Percent
42
1
2.3
2.3
2.3
43
1
2.3
2.3
4.5
46
2
4.5
4.5
9.1
47
2
4.5
4.5
13.6
48
1
2.3
2.3
15.9
49
2
4.5
4.5
20.5
1
50
2
4.5
4.5
25.0
51
4
9.1
9.1
34.1
52
2
4.5
4.5
38.6
54
5
11.4
11.4
50.0
55
4
9.1
9.1
59.1
56
3
6.8
6.8
65.9
57
4
9.1
9.1
75.0
58
1
2.3
2.3
77.3
60
1
2.3
2.3
79.5
61
3
6.8
6.8
86.4
62
1
2.3
2.3
88.6
64
2
4.5
4.5
93.2
65
1
2.3
2.3
95.5
68
1
2.3
2.3
97.7
69
1
2.3
2.3
100.0
44
100.0
100.0
Total
2
1) What is the 5 number summary of this data (min, lower quartile, median, upper
quartile, max)?
The “5 number summary” of a data set includes the minimum, lower
quartile, median, upper quartile and maximum values of the set.
Minimum = 42
Lower Quartile = 50.25
Median = 54.50
Upper Quartile = 57.75
Maximum = 69
2) Who was the oldest president at inauguration? Who was the youngest?
The oldest president was Ronald Reagan at 69
The youngest president was Theodore Roosevelt at 42
3) What was the mean age at inauguration?
The mean age at inauguration was 54.64
3
4) How does Barack Obama compare to the mean? Was his age at inauguration
within one standard deviation of the mean?
Barack Obama was 47 years old at inauguration. This is below the mean
value of 54.64.
Since the standard deviation is 6.273, an age must be within the range from
(54.64 – 6.273) = 48.37 through (54.64 + 6.273) = 60.91 to be within one
standard deviation of the mean. Obama’s age of 47 is outside of this range,
so it is not within one standard deviation of the mean.
5) How many presidents have been more than 2 standard deviations from this mean?
Who were they?
An age must be within the range from (54.64 – 2*6.273) = 42.09 through
(54.64 + 2*6.273) = 67.19 to be within two standard deviations of the mean.
Obama’s age of 47 is outside of this range.
There are three presidents outside of this range: Theodore Roosevelt (42),
William Henry Harrison (68) and Ronald Reagan (69).
6) Looking at your frequencies table, estimate the 90th percentile of this data to the
nearest year. How did you determine this value?
Since 90% of the values must be less than the 90th percentile value, I take the
number of data values – which is 44 – and multiple by 90% = 39.6. So, this
means that 39 values must be less than the 90th percentile value. So, I will
take the value in the 40th position of the sorted set (since there are 39 values
less than the value in the 40th position of the sorted data). The value in the
40th position of the sorted data set is 64. So the 90th percentile of the ages at
inauguration is 64 years old.
7) Looking at the Histogram you got. Is it a basic Histogram (one bar for each
value) or is a Bin Histogram (multiple values per bar)? If it is binned, then how
many ages are there per bin (that is, per bar)?
There are 5 bars in this Histogram for every 10 years of data (5 bars between
50 and 60 and 5 bars between 60 and 70), so each bar must represent 2 years
of age data. Thus, the histogram is binned with 2 years of data per bin.
8) Are presidents inaugurated since Theodore Roosevelt, on average, older or
younger than presidents inaugurated before Roosevelt? Create two modified data
sets and calculate these two means. Copy and paste the results into your Word
file.
4
Using copy-and-paste, I created two new data sets in PASW – the first one
containing data for presidents before Theodore Roosevelt and the second one
containing all data for presidents after Theodore Roosevelt. For each of
these data sets I ran Descriptive Statistics in PASW. The resulting data sets
and PASW statistics results are shown below.
From these results we can see that presidents before Theodore Roosevelt had
a mean age at inauguration of 55.0, while presidents after Theodore
Roosevelt had a mean age at inauguration of 54.83.
New Data Set #1 – Presidents before Theodore Roosevelt
Descriptive Statistics
N
Minimum
Age at Inauguration
25
Valid N (listwise)
25
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
57.00
61.00
57.00
57.00
58.00
57.00
61.00
54.00
68.00
51.00
49.00
64.00
50.00
48.00
65.00
52.00
56.00
46.00
54.00
49.00
George Washington
John Adams
Thomas Jefferson
James Madison
James Monroe
John Quincy Adams
Andrew Jackson
Martin Van Buren
William Henry Harrison
John Tyler
James K. Polk
Zachary Taylor
Millard Fillmore
Franklin Pierce
James Buchanan
Abraham Lincoln
Andrew Johnson
Ulysses S. Grant
Rutherford B. Hayes
James A. Garfield
46.00
Maximum
68.00
Mean
55.0000
Std. Deviation
5.74456
5
21
22
23
24
25
Chester A. Arthur
Grover Cleveland
Benjamin Harrison
Grover Cleveland
William McKinley
50.00
47.00
55.00
55.00
54.00
New Data Set #2
Descriptive Statistics
N
Minimum
Age at Inauguration
18
Valid N (listwise)
18
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
William Howard Taft
Woodrow Wilson
Warren G. Harding
Calvin Coolidge
Herbert Hoover
Franklin Roosevelt
Harry S. Truman
Dwight D. Eisenhower
John F. Kennedy
Lyndon B. Johnson
Richard M. Nixon
Gerald Ford
Jimmy Carter
Ronald Reagan
George H. W. Bush
Bill Clinton
George W. Bush
Barack Obama
43.00
Maximum
69.00
Mean
54.8333
Std. Deviation
6.58206
51.00
56.00
55.00
51.00
54.00
51.00
60.00
62.00
43.00
55.00
56.00
61.00
52.00
69.00
64.00
46.00
54.00
47.00
Part II Crosstab
SMOKE * SEX01 Crosstabulation
6
Count
SEX01
Male
SMOKE
Female
Total
Yes
331
449
780
No
911
1330
2241
1242
1779
3021
Total
1) From this data, answer the questions: What percentage of men smoke? What
percentage of women smoke?
331 men smoke out of a total of 1242 men, so the percentage of men who smoke is
331/1242 = 0.2665 = 26.65%. 449 women smoke out of a total of 1779 women, so the
percentage of women who smoke is 449/1779 = 0.2524 = 25.24%.
SMOKE * INC4GP Crosstabulation
Count
INC4GP
<$20K
SMOKE
Total
$20-40K
$40-70K
over $70K
Refused
Do not know
Total
Yes
125
258
199
127
49
19
777
No
245
625
633
512
165
56
2236
370
883
832
639
214
75
3013
2)
7