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Statistics: Mean, Median, and Range of Two Data Sets

For the following exercise, complete the following:

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

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

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?

There is no mode.
There are two modes.
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.

The 29th percentile is greater than the 30th percentile.
The median is greater than the first quartile.
The third quartile is greater than the first quartile.
The mean is equal to the median.
The range is zero.
Note:

Instructions: Use only the data meant for each question for your calculation. In the past, some students used the data set in question number #1 to answer questions #2 and #3. If you do that, you will be off track.

Solution Preview

1. 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

For the following exercise, complete the following:

Find the mean, median, and range for each of the two data sets.
To find the mean of each data set, we add up the ages in each set and divide it by the number of ages we have.
Mean1 = (57+61+57+57+58+57+61) / 7 = 58.286
Mean2 = (61+52+69+64+46+54+47) / 7 = 56.143
To find the median of a set, we arrange it from smallest to largest and find the one in the center. That is, the median is the "middle" number of the set.
Median1 = 57
Median2 = 54
To find the range, we subtract the smallest value from the largest value of each set.
Range1 = 61- 57 = 4
Range2 = 69-46 = 23

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

The ...

Solution Summary

This solution provides caluclations and discusses the two statements in part (2) and (3) in approximately 800 words.

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