. For the following exercise, complete the following:

a. Find the mean, median, and range for each of the two data sets.

b. Find the standard deviation using the rule of thumb for each of the data sets.

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

1.the mean is 58.286

1.the median is 57
1.the range is 4
The standard deviation for The first data set is8.116

can you do the problm out so i know how you got these numbers? Thanks

a. To find the mean, median, and range for each data set, you will follow these steps:

1. Mean: To find the mean, add up all the values in the data set and divide the sum by the total number of values. In this case, for each data set, add up all the ages and then divide by 7 (since there are 7 values in each set).

For the first 7 data set:
Mean = (57 + 61 + 57 + 57 + 58 + 57 + 61) / 7 = 408 / 7 = 58.29 (approximately)

For the second 7 data set:
Mean = (61 + 52 + 69 + 64 + 46 + 54 + 47) / 7 = 393 / 7 = 56.14 (approximately)

2. Median: To find the median, you need to arrange the values in ascending order and then find the middle value. If there is an even number of values, take the average of the two middle values.

For the first 7 data set:
Arranged in ascending order: 57, 57, 57, 57, 58, 61, 61
Median = 57 (since there is an odd number of values)

For the second 7 data set:
Arranged in ascending order: 46, 47, 52, 54, 61, 64, 69
Median = 54 (since there is an odd number of values)

3. Range: To find the range, subtract the minimum value from the maximum value.

For the first 7 data set:
Range = 61 - 57 = 4

For the second 7 data set:
Range = 69 - 46 = 23

b. To find the standard deviation using the rule of thumb, follow these steps:

1. Calculate the mean as found in step a.

For the first 7 data set: Mean = 58.29 (approximately)
For the second 7 data set: Mean = 56.14 (approximately)

2. Find the absolute deviation of each value from the mean. To do this, subtract the mean from each value, then take the absolute value.

For the first 7 data set:
|57 - 58.29| = 1.29
|61 - 58.29| = 2.71
|57 - 58.29| = 1.29
|57 - 58.29| = 1.29
|58 - 58.29| = 0.29
|57 - 58.29| = 1.29
|61 - 58.29| = 2.71

For the second 7 data set:
|61 - 56.14| = 4.86
|52 - 56.14| = 4.14
|69 - 56.14| = 12.86
|64 - 56.14| = 7.86
|46 - 56.14| = 10.14
|54 - 56.14| = 2.14
|47 - 56.14| = 9.14

3. Calculate the standard deviation using the formula:
Standard Deviation = (Sum of squared absolute deviations) / (Total number of values - 1)

For the first 7 data set:
Sum of squared absolute deviations = (1.29^2 + 2.71^2 + 1.29^2 + 1.29^2 + 0.29^2 + 1.29^2 + 2.71^2) = 23.43
Standard Deviation = 23.43 / (7 - 1) = 3.91 (approximately)

For the second 7 data set:
Sum of squared absolute deviations = (4.86^2 + 4.14^2 + 12.86^2 + 7.86^2 + 10.14^2 + 2.14^2 + 9.14^2) = 518.71
Standard Deviation = 518.71 / (7 - 1) = 86.45 (approximately)

c. Comparing the two data sets, we can observe the following differences:

- The mean age of the first 7 presidents is higher (58.29) compared to the mean age of the second 7 presidents (56.14).
- The median age for both data sets is relatively close, with the first 7 presidents having a median of 57, and the second 7 presidents having a median of 54.
- The range for the first 7 presidents is smaller (4) compared to the range for the second 7 presidents (23).
- The standard deviation for the second 7 presidents (86.45) is significantly larger than the standard deviation for the first 7 presidents (3.91). This indicates a higher dispersion of ages in the second set, suggesting a greater difference between individual ages and the mean.

In summary, the two data sets show differences in mean, range, and standard deviation, indicating variations in the ages of the two groups of presidents.