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

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

3. 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

Which part of this assignment don't you understand?

mean?
median?
range?
standard deviation?

how to do the problem? I'm lost

First do this:

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

The mean is the average. Add each set of numbers together and divide by 7 to find the mean.

The median is the middle number. Arrange each set in numerical order and find the middle number.

The range is the difference between the highest number and the lowest number.

http://www.purplemath.com/modules/meanmode.htm

Please post your answers, and I'll help you with the rest of this assignment.

The range rule of thumb says that the range is approximately four times the standard deviation.

To find the mean, median, and range for each data set and to calculate the standard deviation using the rule of thumb, follow these steps:

1. Calculating the mean:
- Add up all the numbers in the data set
- Divide the sum by the total number of data points

For the first data set (First 7):
- Sum = 57 + 61 + 57 + 57 + 58 + 57 + 61 = 408
- Number of data points = 7
- Mean = Sum / Number of data points = 408 / 7 = 58.29 (rounded to two decimal places)

For the second data set (Second 7):
- Sum = 61 + 52 + 69 + 64 + 46 + 54 + 47 = 393
- Number of data points = 7
- Mean = Sum / Number of data points = 393 / 7 = 56.14 (rounded to two decimal places)

2. Calculating the median:
- Arrange the numbers from the data set in ascending order
- If there is an odd number of data points, the median is the middle value
- If there is an even number of data points, the median is the average of the two middle values

For the first data set (First 7):
- Arranged data set: 57, 57, 57, 58, 61, 61
- Median = 57

For the second data set (Second 7):
- Arranged data set: 46, 47, 52, 54, 61, 64, 69
- Median = 54

3. Calculating the range:
- Subtract the smallest value from the largest value in the data set

For the first data set (First 7):
- Minimum value = 57
- Maximum value = 61
- Range = Maximum value - Minimum value = 61 - 57 = 4

For the second data set (Second 7):
- Minimum value = 46
- Maximum value = 69
- Range = Maximum value - Minimum value = 69 - 46 = 23

4. Calculating the standard deviation using the rule of thumb:
- Subtract the mean from each data point and square the result
- Calculate the mean of these squared differences
- Take the square root of the mean squared differences

For the first data set (First 7):
- Differences from the mean: (-1.29)^2, 2.71^2, (-1.29)^2, (-1.29)^2, (-0.29)^2, (-1.29)^2, 2.71^2
- Mean squared difference = (1.6649 + 7.3441 + 1.6649 + 1.6649 + 0.0841 + 1.6649 + 7.3441) / 7 = 3.012
- Standard deviation ≈ Square root of the mean squared difference ≈ √3.012 ≈ 1.735 (rounded to three decimal places)

For the second data set (Second 7):
- Differences from the mean: 4.86^2, (-3.14)^2, 12.86^2, 7.86^2, (-10.14)^2, (-2.14)^2, (-9.14)^2
- Mean squared difference = (23.6196 + 9.8596 + 165.6196 + 61.5396 + 102.8196 + 4.5796 + 83.5396) / 7 = 58.3885
- Standard deviation ≈ Square root of the mean squared difference ≈ √58.3885 ≈ 7.638 (rounded to three decimal places)

Comparing the two sets:
- The mean age of the first data set (First 7) is 58.29, while the mean age of the second data set (Second 7) is 56.14.
- The median age of the first data set (First 7) is 57, while the median age of the second data set (Second 7) is 54.
- The range of the first data set (First 7) is 4, while the range of the second data set (Second 7) is 23.
- The standard deviation of the first data set (First 7) is approximately 1.735, while the standard deviation of the second data set (Second 7) is approximately 7.638.

Based on these comparisons, you can observe that the mean and median ages are slightly higher in the first data set (First 7) compared to the second data set (Second 7). The range is also smaller in the first data set. Additionally, the standard deviation is significantly higher in the second data set, indicating a wider spread of ages compared to the first data set.