Central Tendency Chapter 3 (part 3)

The Mode The mode is defined to be the value that occurs most often in a data set. A data set can have more than one mode. A data set is said to have no mode if all values occur with the same frequency. 38

The Mode - Examples The following data represent the duration (in days) of U.S. space shuttle voyages for the years 1992-94. Find the mode. Data set: 8, 9, 9, 14, 8, 8, 10, 7, 6, 9, 7, 8, 10, 14, 11, 8, 14, 11. Ordered set: 6, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 10, 10, 11, 11, 14, 14, 14. Mode = 8. 39

The Mode - Examples Six strains of bacteria were tested to see how long they could remain alive outside their normal environment. The time, in minutes, is given below. Find the mode. Data set: 2, 3, 5, 7, 8, 10. There is no mode since each data value occurs equally with a frequency of one. 40

The Mode - Examples Eleven different automobiles were tested at a speed of 15 mph for stopping distances. The distance, in feet, is given below. Find the mode. Data set: 15, 18, 18, 18, 20, 22, 24, 24, 24, 26, 26. There are two modes (bimodal). The values are 18 and 24. Why? Bimodal distributions usually show that there are two distinct groups of individuals within the same sample or population (e.g. males and females within a group of participants). 41

Which measure to use? Mean Median Mode Uses every score in the distribution Good representation Valuable for inferential statistics Median With skewed distributions and extreme scores Useable with undetermined scores Ordinal data Mode Used for data on nominal scales With discrete variables (can’t have 2.5 children) Mean Before we discuss this we must note that in most cases several measures of central tendency can be used. Also the mean is usually the preferred measure of central tendency, since it used every score in the distribution it can usually be a good representation. It is also closely related to standard deviation and variance, all factors that are a part of variablility which we will discuss in the next chapter. This makes it valuable for inferential statistics. Median In skewed distributions one or two scores may have a huge influence and cause the mean to be displaced. Here the fact that the mean uses all the scores is a disadvantage 49

Mean, Median, and Mode Which do you use? Mean is most preferred because it uses every score in a distribution, also because it is closely related to variance and standard deviation (next chapter). Sometimes not feasible because it is not particularly representative. Median is used when there are extreme scores or a skewed distribution. Also when there are undetermined values or in open ended distributions. Sometimes better preferred with ordinal level of data. Mode is used when the measurement is on a nominal scale, when variables are discrete. Used as an additional measure to describe shape of the distribution because it indicates the location of the peak in the distribution.

Distribution Shapes Frequency distributions can assume many shapes. The first important aspect is the number of “peaks”—also called the “mode” of the distribution 49

Remember?

Unimodal Distributions A Normal Distribution has only one high point, and each side goes down at the same rate

The population distribution of IQ scores: an example of a normal distribution – Smooth Curves