LSP 121-405 In-Class Activity 5 Working with PASW 20 points Due by Saturday, Oct. 17 th 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 Frequency Percent Valid Percent Cumulative Percent Valid 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 Total 44 100.0 100.0 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 90 th percentile of this data to the nearest year. How did you determine this value? Since 90% of the values must be less than the 90 th 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 90 th percentile value. So, I will take the value in the 40 th position of the sorted set (since there are 39 values less than the value in the 40 th position of the sorted data). The value in the 40 th position of the sorted data set is 64. So the 90 th 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 Maximum Mean Std. Deviation Age at Inauguration 25 46.00 68.00 55.0000 5.74456 Valid N (listwise) 25 1 George Washington 57.00 2 John Adams 61.00 3 Thomas Jefferson 57.00 4 James Madison 57.00 5 James Monroe 58.00 6 John Quincy Adams 57.00 7 Andrew Jackson 61.00 8 Martin Van Buren 54.00 9 William Henry Harrison 68.00 10 John Tyler 51.00 11 James K. Polk 49.00 12 Zachary Taylor 64.00 13 Millard Fillmore 50.00 14 Franklin Pierce 48.00 15 James Buchanan 65.00 16 Abraham Lincoln 52.00 17 Andrew Johnson 56.00 18 Ulysses S. Grant 46.00 19 Rutherford B. Hayes 54.00 20 James A. Garfield 49.00 5
21 Chester A. Arthur 50.00 22 Grover Cleveland 47.00 23 Benjamin Harrison 55.00 24 Grover Cleveland 55.00 25 William McKinley 54.00 New Data Set #2 Descriptive Statistics N Minimum Maximum Mean Std. Deviation Age at Inauguration 18 43.00 69.00 54.8333 6.58206 Valid N (listwise) 18 27 William Howard Taft 51.00 28 Woodrow Wilson 56.00 29 Warren G. Harding 55.00 30 Calvin Coolidge 51.00 31 Herbert Hoover 54.00 32 Franklin Roosevelt 51.00 33 Harry S. Truman 60.00 34 Dwight D. Eisenhower 62.00 35 John F. Kennedy 43.00 36 Lyndon B. Johnson 55.00 37 Richard M. Nixon 56.00 38 Gerald Ford 61.00 39 Jimmy Carter 52.00 40 Ronald Reagan 69.00 41 George H. W. Bush 64.00 42 Bill Clinton 46.00 43 George W. Bush 54.00 44 Barack Obama 47.00 Part II Crosstab SMOKE * SEX01 Crosstabulation 6
Count Male SEX01 Female Total SMOKE Yes 331 449 780 No 911 1330 2241 Total 1242 1779 3021 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%. Count SMOKE * INC4GP Crosstabulation INC4GP <$20K $20-40K $40-70K over $70K Refused Do not know Total SMOKE Yes 125 258 199 127 49 19 777 No 245 625 633 512 165 56 2236 Total 370 883 832 639 214 75 3013 2) 7