c. Compare the two sets and describe what you discover.
The following data sets shows the ages of the first seven presidents (President Washington through President Jackson) and the seven most recent presidents including President Obama. Age is given at time of inauguration.
First 7: 57 61 57 57 58 57 61
Second 7: 61 52 69 64 46 54 47
I think I would calculate the mean, standard deviation (n-1), and range.
You might even then do a statistical test.
Find the mean first = sum of scores/number of scores
Subtract each of the scores from the mean and square each difference. Find the sum of these squares. Divide that by the number of scores to get variance.
Standard deviation = square root of variance
To compare difference between means:
Ho: mean1 = mean2
Ha: mean1 ≠ mean2
Z = (mean1 - mean2)/standard error (SE) of difference between means
SEdiff = √(SEmean1^2 + SEmean2^2)
SEm = SD/√(n-1)
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to the Z score to find if the difference is significant.
To compare the two sets and describe what you discover, you can start by calculating some basic statistics. In this case, you have two sets of age data for the first seven presidents and the seven most recent presidents.
First, let's find the mean (average) age for each set. To do this, add up all the ages and divide the total by the number of values.
For the first set:
Mean = (57 + 61 + 57 + 57 + 58 + 57 + 61) / 7 = 413 / 7 = 59
For the second set:
Mean = (61 + 52 + 69 + 64 + 46 + 54 + 47) / 7 = 393 / 7 ≈ 56.14
Next, let's find the median age for each set. The median is the middle value in a set when it is arranged in ascending order.
For the first set:
Arranging the ages in ascending order: 57, 57, 57, 57, 58, 61, 61
Median = 57 (the middle value)
For the second set:
Arranging the ages in ascending order: 46, 47, 52, 54, 61, 64, 69
Median = 54 (the middle value)
Now, let's compare the means and medians of the two sets:
- The mean age of the first set is 59, while the mean age of the second set is approximately 56.14. This means that, on average, the first set of presidents had slightly higher ages at their time of inauguration compared to the second set.
- The median age of the first set is 57, while the median age of the second set is 54. This indicates that the middle value in the second set is lower than in the first set. Therefore, the second set overall consists of younger presidents at their time of inauguration compared to the first set.
In summary, when comparing the two sets of ages, we find that the second set of presidents (the most recent ones) generally had lower average and median ages at the time of their inauguration compared to the first set of presidents.