Measures of Central Tendency

1) A measure of central tendency in a set of data is a tool that defines a typical piece of data. In a group of three students, brainstorm as many different measures of central tendency as you can come up with. Write an algorithm for finding each measure of central tendency. An algorithm is a step by step procedure for completing a task. Your algorithms should be very clear and be able to be followed by someone who is not in your group. If you come up with an uncommon measure, give it a name that you think makes sense, based on what it is or what it does.

If you finish these tasks before other groups, first try to come up with more creative measures of central tendency. If you still have time after you have exhausted your creativity, list the benefits and drawbacks of each of your measures. Be sure to highlight the types of data for which it is appropriate, discussing both numeric and contextual issues. List circumstances in which each measure might be preferable over the other measures you came up with.

I may interrupt you to have you write your more creative algorithms on butcher paper to share with the class.

2) A useful tool in finding some measures of central tendency is the rank of a piece of data. The rank is found by sorting the data from smallest to largest, and assigning each data piece the number associated with its place in the list. The smallest number has a rank of 1, the second smallest number has a rank of 2, and so on, all the way up to the largest number, which has a rank of n.

A common problem related to measures of central tendency is how to use n to find the rank of the median. Create an algorithm for finding the rank of the median of a set of data. Use the data sets below to check to see if your algorithm works. Adjust your algorithm if it does not find the correct rank of the median for each set.

Data set one: 17 19 22 31 42

Data set two: 26 29 38 39 41 47 48 52 64 67

Data set three: 11 24 26 28 35 37 45 48 59 61 63

Data set four: 58 60 71 75 81 86 88 92

3) Statisticians are often interested in not only in finding the median, or half way point in a set of data, but also in finding the data point that is one-quarter of the way through the data and the data point that is three-quarters of the way through the data. These two points are called the first and third quartiles. Though not frequently referred to as such, the median is actually the second quartile of a set of data.

Using n to find the rank of the quartiles of a set of data is an interesting problem that does not provide such agreed-upon algorithms as those we discovered for finding the rank of the median. Create an algorithm for finding the rank of the quartiles of a set of data. Use the data sets above to check to see if your algorithm works. Adjust your algorithm if it does not find a reasonable rank of the quartiles for each set. Discuss the benefits of your algorithm over others.

If you finish these tasks before other groups, try to come up with more algorithms for finding the quartiles. Then list the benefits and drawbacks of each of your algorithms. Be sure to highlight the types of data for which it is appropriate, discussing both numeric and contextual issues. List circumstances in which each algorithm might be preferable over others.