What does the Mean, Median, Mode and Range tell us about the data? Central Tendency What does the Mean, Median, Mode and Range tell us about the data?

What additional information would you like? What is "central tendency," and why do we want to know the central tendency of a group of scores? Central Tendency is the point at which the distribution is in balance. Imagine this situation: You are in a class with just four other students, and the five of you took a 5-point pop quiz. Today your instructor is walking around the room, handing back the quizzes. She stops at your desk and hands you your paper. Written in bold black ink on the front is "3/5." How do you react? Are you happy with your score of 3 or disappointed? How do you decide? You might calculate your percentage correct, realize it is 60%, and be appalled. But it is more likely that when deciding how to react to your performance, you will want additional information. What additional information would you like?

You know you gone… Look at someone’s paper to see their score Ask me, Mrs. Cole who got the high score? Try to find out how everyone else did… Your questions are all about central tendency

3 different ways to look at your score Student Dataset A Dataset B Dataset C You 3 John's 4 2 Maria's Shareecia's Luther's 5 1 Table 1. They are labeled "Dataset A," "Dataset B," and "Dataset C." Which of the three datasets would make you happiest? In other words, in comparing your score with your fellow students' scores, in which dataset would your score of 3 be the most impressive?

center of the distribution. Student Dataset A Dataset B Dataset C You 3 John's 4 2 Maria's Shareecia's Luther's 5 1 Data set A- Your score and everyone's score is the Center of distribution. Data set B- Your score is below the center of distribution. Data set C- yours is above the center of distribution. Who has figured out the WHAT the center of distribution is? Is the Center of distribution the same for each set of data?

Measures of Central tendency The mean- The median The mode Lets watch the video to decide how to use them. http://onlinestatbook.com/2/summarizing_distributions/measuresM.html

Picture of the mean Balance Scale One definition of central tendency is the point at which the distribution is in balance. Figure 2 shows the distribution of the five numbers 2, 3, 4, 9, 16 placed upon a balance scale. If each number weighs one pound, and is placed at its position along the number line, then it would be possible to balance them by placing a fulcrum at 6.8.

median The median is the 50th percentile of a distribution. To find the median of a number of values, first order them, then find the observation in the middle: the median of 5, 2, 7, 9, and 4 is 5. (Note that if there is an even number of values, one takes the average of the middle two: the median of 4, 6, 8, and 10 is 7.) The median is often more appropriate than the mean in skewed distributions and in situations with outliers.

mode The mode is a measure of central tendency. It is the most frequent value in a distribution: the mode of 3, 4, 4, 5, 5, 5, 8 is 5. Note that the mode may be very different from the mean and the median.

Let’s not forget about … RANGE!! The difference between the maximum and minimum values of a variable or distribution. The range is the simplest measure of variability.