Comparing Variations:

1. 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

2. A data set consists of a set of numerical values. Which, if any, of the following statements could be correct?

a. There is no mode.
b. There are two modes.
c. There are three modes.

3. Indicate whether the given statement could apply to a data set consisting of 1,000 values that are all different.

a. The 29th percentile is greater than the 30th percentile.
b. The median is greater than the first quartile.
c. The third quartile is greater than the first quartile.
d. The mean is equal to the median.
e. The range is zero.

I will be happy to critique your thinking.

can u still help?

58.28

Compare the two sets and describe what you discover

. 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.

a. To find the mean, median, and range for each data set, follow these steps:
- Mean: Calculate the sum of all the values in the data set and divide it by the number of values. This will give you the average or mean.
- Median: Arrange the values in ascending order and find the middle value. If there is an odd number of values, the median is the middle value. If there is an even number of values, the median is the average of the two middle values.
- Range: Subtract the smallest value from the largest value in the data set.

For the first data set (First 7):
Mean = (57 + 61 + 57 + 57 + 58 + 57 + 61) / 7
Median = 57
Range = Largest value - Smallest value

For the second data set (Second 7):
Mean = (61 + 52 + 69 + 64 + 46 + 54 + 47) / 7
Median = 54
Range = Largest value - Smallest value

b. To find the standard deviation using the rule of thumb for each data set, follow these steps:
- Calculate the mean of the data set.
- Subtract the mean from each value in the data set and square the result.
- Find the average of the squared differences.
- Take the square root of the average to get the standard deviation.

Note: The rule of thumb method divides the range by 4 to estimate the standard deviation. This is a rough estimation and may not be as accurate as other methods.

For the first data set (First 7):
- Find the range (already calculated in part a).
Standard Deviation = Range / 4

For the second data set (Second 7):
- Find the range (already calculated in part a).
Standard Deviation = Range / 4

c. Compare the two sets and describe what you discover:
- Compare the mean, median, range, and standard deviation of the two data sets.
- Look for similarities and differences in central tendency (mean, median) and variability (range, standard deviation).
- Consider whether one data set has values that are consistently higher or lower than the other.

2.

a. There is no mode: The mode is the value(s) that appear most frequently in a data set. If there is no value that appears more than once, there is no mode.

b. There are two modes: The mode is the value(s) that appear most frequently in a data set. If there are two or more values that appear with the same highest frequency, there can be more than one mode.

c. There are three modes: The mode is the value(s) that appear most frequently in a data set. If there are three or more values that appear with the same highest frequency, there can be more than one mode.

In this case, without the specific data set, it is not possible to determine which statement is correct.

3.

a. The 29th percentile is greater than the 30th percentile: Percentiles represent the relative position of a value within a data set. In a data set with 1,000 different values, each percentile will represent a different value. Therefore, it is possible for the 29th percentile to be greater than the 30th percentile.

b. The median is greater than the first quartile: The median is the middle value of a data set, and the first quartile represents the 25th percentile. If the data set is arranged in ascending order, it is possible for the median to be greater than the first quartile.

c. The third quartile is greater than the first quartile: The first quartile represents the 25th percentile, and the third quartile represents the 75th percentile. If the data set is arranged in ascending order, it is possible for the third quartile to be greater than the first quartile.

d. The mean is equal to the median: In a data set with 1,000 different values, the mean and median can be equal, but it is not guaranteed. It depends on the distribution of the values.

e. The range is zero: The range is calculated by subtracting the smallest value from the largest value in a data set. If all 1,000 values in the data set are different, the range cannot be zero.