Final answer:
The mean of the ages of the P.T.A. Presidents is 56. The mode is 62 and the median is also 56. The mean for the ages of Campbell, Jackson, Johnson, Fearon, and McLean is 56.4. The median for the ages of Harper, Taylor, Hacker, Powell, and Ellis is 56.
Step-by-step explanation:
To find the mean of a set of data, we add up all the values and divide by the number of values. For the ages of the P.T.A. Presidents, we have:
62 + 43 + 55 + 56 + 62 + 52 + 68 + 62 + 54 + 46 = 560.
There are 10 presidents, so the mean age is 560 / 10 = 56.
The mode is the value that appears the most in the data. In this case, the mode is 62 because it appears the most number of times, which is 3.
The median is the middle value in the sorted data. Since there are 10 presidents, the median will be the average of the 5th and 6th values. Sorting the ages in ascending order, we get:
43, 46, 52, 54, 55, 56, 62, 62, 62, 68.
The 5th and 6th values are both 56, so the median is 56.
To find the mean for the ages of Campbell, Jackson, Johnson, Fearon, and McLean, we add up their ages and divide by the number of presidents. The ages are:
62 + 43 + 55 + 54 + 68 = 282.
There are 5 presidents, so the mean age is 282 / 5 = 56.4.
The median for the ages of Harper, Taylor, Hacker, Powell, and Ellis can be found the same way. Their ages are:
52 + 62 + 62 + 56 + 55 = 287.
There are 5 presidents, so the median will be the average of the 3rd and 4th values. Sorting the ages in ascending order, we get:
52, 55, 56, 62, 62.
The 3rd and 4th values are both 56, so the median is 56.