1. For the following exercise, complete the following by using the data sets below that provides the ages of the first seven presidents:
a. Find the mean, median, and range for each of the two data sets.
First 7: The mean is 58.3
The median is 57
The range is 4
Second 7: The mean is 56.1
The median is 64
The range is 23
b. Find the standard deviation using the range rule of thumb for each of the data sets. Please show your work. (Please see Chapter 4, Section 4.3, page 173 of the text).
low value ¡Ö mean ¨C (2 ¡Á range/4)
high value ¡Ö mean + (2 ¡Á range/4)
First 7:
Low value ¡Ö 58.3 ¨C (2 ¡Á 4/4) ¡Ö 58.3-(2¡Á1) ¡Ö58.3-2¡Ö56.3
High value ¡Ö 58.3 + (2 ¡Á 4/4) ¡Ö58.3+ (2¡Á1) ¡Ö 58.3+2¡Ö60.3
Second 7:
Low value ¡Ö 56.1 ¨C (2 ¡Á 23/4) ¡Ö56.1-(2¡Á5.75) ¡Ö 56.1- 11.5¡Ö44.6
High value ¡Ö 56.1 + (2 ¡Á 23/4) ¡Ö 56.1+(2¡Á5.75) ¡Ö56.1+11.5¡Ö67.6
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 am not sure if these answers are right and how to compare and describe the information?
a. is right except second 7 median = 54. (typo?)
b. I am not sure what your symbols mean, so I cannot comment.
To find the mean, median, and range for each data set, you can follow these steps:
1. Mean: Add up all the numbers in the data set and divide by the total count of numbers.
For the first data set ("First 7"):
Mean = (57 + 61 + 57 + 57 + 58 + 57 + 61) / 7 = 58.3
For the second data set ("Second 7"):
Mean = (61 + 52 + 69 + 64 + 46 + 54 + 47) / 7 = 56.1
2. Median: Arrange the numbers in ascending order and find the middle value. If there are two middle values, calculate their average.
For the first data set:
Arranged in ascending order: 57, 57, 57, 58, 61, 61
Median = 57
For the second data set:
Arranged in ascending order: 46, 47, 52, 54, 61, 64, 69
Median = 64
3. Range: Find the difference between the highest and lowest values in the data set.
For the first data set:
Range = Highest value - Lowest value = 61 - 57 = 4
For the second data set:
Range = Highest value - Lowest value = 69 - 46 = 23
To find the standard deviation using the range rule of thumb, you can use the following formula:
Standard deviation ≈ (High value - Low value) / 4
For the first data set:
Standard deviation ≈ (60.3 - 56.3) / 4 = 4 / 4 = 1
For the second data set:
Standard deviation ≈ (67.6 - 44.6) / 4 = 23 / 4 = 5.75
Comparing the two sets, we can see the following:
- The mean age of the first seven presidents (58.3) is slightly higher than the mean age of the second seven presidents (56.1).
- The median age of the second set (64) is higher than the median age of the first set (57).
- The range of ages in the second set (23) is higher than the range in the first set (4).
- The standard deviation of ages in the second set (5.75) is higher than the standard deviation in the first set (1).
This comparison shows that the second set of presidents has a wider range of ages and more variability compared to the first set, which is reflected in the higher standard deviation.