Chapter 3-Central Tendency: Lecture

Question 1

Central tendency

Answer 1

• a statistical measure that uses a single value to describe the center of distribution
• goal is to identify the single value that best represents the entire dataset
• can condense a large set of data into a single value

determined using several well-defined procedures

no single procedure always produces a good represtative value

Question 2

What are the most common techniques for measuring central tendency?

Answer 2

Mean, median, and mode

Question 3

Descriptive Statistic

Answer 3

• describes a set of data in a simple, concise form
• it is possible to compare two (or more) sets of data by comparing the average score

Question 4

The mode

Answer 4

• the most frequently occuring score or class inerval in the distribution
• in a frequency distribution, the mode corresponds to the highest point of the distribution
• can be determined for nom. ord. int. and rat. data
• often is used as supplemental measure of central tendency for ord. int. and rat. data (along w/ the median or mean)

Question 5

What measure of central tendency can be used for data measured on the nominal scale?

Answer 5

ONLY the mode

Question 6

bimodial vs. multimodial

Answer 6

bimodial distribution: 2 modes
multimodial distribution: 3+ modes

Question 7

Minor and major mode

Answer 7

• The general term mode is also used to describe a peak in a distribution that is not necessarily the highest point.
• Distribution may have a major mode at the highest peak and a minor mode at the secondary peak, when distribution is CLEARLY humped

Question 8

The median

Answer 8

• divies the scores so that 50% have values = to or less than the median
• if scores are listed from smallest to largest, the median is the midpoint of the list
• requires scores that can be placed in rank order and measured by ord, int, or rat scale

Question 9

Calculating median

Answer 9

• If odd # of scores, median is the middle score
• If even # of scores, the median is the 2 middle scores… add them and divide by 2

Question 10

Advantage to the median

Answer 10

• Is relatively unaffected by extreme scores
• tends to stay in the center of the distrbution even there are a few extreme scores ,or the distribution is very skewed; in these situations the median is a good alternative to the mean

Question 11

Mean

Answer 11

• calculate by adding all the scores and dividing that total by the # of scores
• Mean for pop. represented by mu, mean for sample represented by M (or x bar)
• can be used for ord, int, and ratio data (but is best for int and rat)

Question 12

What is the most commonly used measure of central tendency?

Answer 12

the mean

Question 13

How can the mean be defined conceptually?

Answer 13

• the balance point of the distribution
• the sum of distances below the mean is exactly equal to the sum of the distances above the mean

Question 14

Changing the mean

Answer 14

• because calculation involves every score, changing the value of any score always will change the mean
• discarding or adding new scores will almost always chage the mean (except for when you discard or add a score that is equal to the mean)

Question 15

Adding/subtracting/dividing/multiplying a constant value to every score…

Answer 15

• when adding/subtracting a constant value from every score, the mean is increased or reduced by that same constant value
• when diving and multiplying, the new mean is = to the old mean (x or divided by) that same constant value

Question 16

Mean does not provide a representative value when distribution…

Answer 16

• contains a few extreme scores (like US income)
• is very skewed (like US income)
  … the mean will be pulled toward the tail/toward the extreme scores and will not provide a representative central value

note: cannot compute the mean w nominal data

Question 17

In humped distribution the mean…

Answer 17

might represent no one in the distribution

Question 18

Central tendency and symmetrical distribution

Answer 18

• mean, median, and mode are systematically related
• In a symmetrical distribution, the mean and median are the same
• The mode will also equal the mean and median if there is only one mode

Question 19

Central tendency and skewed distribution

Answer 19

In a skewed distribution…
* mode: located at peak on one side
* mean: usually displaced toward the tail
* median: usually between the mode and the mean