Week 2 Lesson 3 will discuss the appropriate use of measures of central tendency and variability in describing ungrouped set of data.

Topics this Week

Organization of Data

Measures of Central Tendency

Measures of Variability

Key Concepts

Organization of Data

Measures of Central Tendency and Variability

The Mean

The Median

The Mode

Skewed Distributions and Measures of Central Tendency

Read pages 44-52 of your textbook.

Activity 1

With the assigned topic/s to your group, find at least one very good internet site or Url that you think is useful to that topic/s. Discuss in no more than 2 sentences why it is useful; what important lessons will you get from the Url site.

Activity 2

Identify at least one lesson you have learned in this week’s discussion and in brief discuss its importance with your groupmates.

Activity 3

Try working on this example and interprete the results. Submit your assignment via the assignment panel.

Kiwi Bird Problem

As is commonly known, KIWI-birds are native to New Zealand. They are born exactly one foot tall and grow in one foot intervals. That is, one moment they are one foot tall and the next they are two feet tall. They are also very rare. An investigator goes to New Zealand and finds four birds. The mean of the four birds is 4, the median is 3, and the mode is 2. What are the heights of the four birds?

Hint - examine the constraints of the mode first, the median second, and the mean last.

Submit your initial thoughts regarding your research journal paper in relation to the topics we have discussed so far.

Organization of Data

Data can be further classified as ungrouped or grouped. Ungrouped set of data means raw or not arranged in any order, while grouped is data organized and presented in table form. Whether grouped or ungrouped, data can be organized with the help of measure of central tendency, measure of dispersion, and quantiles.

For this lesson, we will be discussing measure of central tendency and measure of variability. But note that there are actually four types of measures : the measure of central tendency, measure of dispersion, validity and reliability. The later two are not covered in this course.

Measures of Central Tendency and Variability

Measures of Central Tendency is also called as Measure of Central or Central Location or Averages. Here, we tend to locate the center of the distribution when the points tend to converge at the center. On the other hand, Measure of Variability is also known as Measure of Dispersion or Spread. Here, we tend to measure how variable the points are from each other or from the center as the points tend to go away from the center of the distribution.

Under the measure of Central tendency we have the mean, the median and the mode, while we the range, the quartile deviation, interquartile deviation, standard deviation, and mean absolute deviation for the Measure of Variability. The diagram below illustrates the measure of central tendency as against the measure of variability.

Measure of Central Tendency Measure of Variability

The Mean

The mean, symbolized by[pic](x with a bar on top) is the sum of the scores divided by the number of scores. The following formula both defines and describes the procedure for finding the mean:

where x is the sum of the scores and n is the number of scores.

Example: The following data shows the number of injections required in First 24 Postoperative hours in 5 patients: 3, 7, 8, 6, 4.

The mean is 5.6 injections.

The use of means as a way of describing a set of scores is fairly common; average income, average weekly allowance, grade point average, and average points scored per game are all means. Note however, the use of the word "average" in all of the above phrases. Average can be used generally and may be regarded as either mean, median or mode. Each of them has it’s own...