U.S. Presidents. The ages of the 44 presidents at their first inauguration (as of 2011) are:
57 57 49 52 50 42 54 55 64
61 61 64 56 47 51 51 56 46
57 54 50 46 55 56 60 61 54
57 68 48 54 55 55 62 52 47
58 51 65 49 54 51 43 69
a. Construct a frequency distribution with a first class of 42-47
b. Construct a histogram
c. Construct a frequency polygon
We cannot construct histograms or frequency polygons on these posts.
If the first class is 42-47, then the remaining classes will also include 6 years: 48-53, 54-59, 60-65, 66-71.
a. To construct a frequency distribution with a first class of 42-47, you need to count the number of presidents whose ages fall within this range. Here is a step-by-step process to do so:
1. Organize the given ages in ascending order: 42 43 46 46 47 47 48 49 49 50 50 51 51 51 52 54 54 55 55 55 56 56 57 57 57 57 58 60 61 61 62 64 64 65 68 69.
2. Count the frequency or number of occurrences of each age within the range 42-47. Here is the frequency distribution table:
Age Range | Frequency
------------------------
42-47 | 3
48-53 | 3
54-59 | 6
60-65 | 7
66-71 | 4
------------------------
b. To construct a histogram, you will need the frequency distribution table from step 'a'. Follow these steps:
1. Determine the range of values. In this case, it would be the difference between the highest and lowest data points. The lowest age is 42, and the highest age is 69, so the range is 69 - 42 = 27.
2. Decide on the number of intervals or classes for your histogram. In this case, let's use 5 intervals.
3. Calculate the width of each interval by dividing the range by the number of intervals. In this case, the width would be 27 / 5 = 5.4 (round it to 5).
4. Use the frequency distribution table (step 'a') to create the horizontal axis labels and vertical bars. The horizontal axis represents age groups, and the vertical axis represents frequency.
5. Plot the frequency for each age group by drawing vertical bars with heights according to the corresponding frequency.
c. To construct a frequency polygon, you will need the frequency distribution table as well. Follow these steps:
1. Use the frequency distribution table (step 'a') to create the horizontal axis labels and vertical points. The horizontal axis represents age groups, and the vertical axis represents frequency.
2. Plot each age group on the horizontal axis and its corresponding frequency on the vertical axis.
3. Connect each plotted point with straight lines to form a polygon.
By following these steps, you can construct a frequency distribution, histogram, and frequency polygon based on the given ages of the U.S. presidents at their first inauguration.