Central tendency (p.62-71)

How is the mean different from median and mode?

More sensitive to extreme scores (outliers) than both median and mode (Pagano, 2001, 65)

When there are ties for the most frequent score, the distribution is _________ if more than two scores tie.

Multimodal

How is mean affected by extreme scores? Skewness?

...

How is median affected by extreme scores? Skewness?

...

How is mode affected by extreme scores? Skewness?

...

MODE

...

Notation for mean (population)

...

Notation for mean (sample)

...

2 characteristics of median?

1) median is less sensitive to extreme scores; median stays the same, whereas mean changes 2) more subject to sampling variability than mean, but less subjective to sampling variability than mode

The best measure of central depends on...

1) scale of measurement 2) shape of distribution

5 characteristics of the mean?

1) sensitive to exact value of all the scores in the distribution 2) sensitive to extreme scores 3) least subject to sampling variation (not very sensitive to different variations, generally consistent, reason why used in inferential statistics) 4) sum of deviations about mean equals zero (if mean subtracted from each source, sum = o) because mean is balance point of distribution 5) Sum of squared deviation of all scores about their mean is a minimum. (see Pagano, 2001, pg. 64-66)

0 modes

A distribution that consists of only one of each score.

Unimodal

A distribution where a single score is most frequent has one mode

When there are ties for the most frequent score the distribution is ______ if two scores tie.

Bimodal

Skew refers to:

GENERAL SHAPE of a distribution when it is graphed.

Best measure of central tendency for ordinal scale:

MEDIAN b/c dealing with rank/order

Best measure of central tendency for nominal scale:

MODE

What are 3 of the most common measures of central tendency?

Mean, Median, and Mode

Best measure of central tendency for interval scale or ratio scale:

Mean, Median, or Mode, depends on shape of distribution

How is median different than mean and mode?

Not affected by extreme scores.

MEAN

Sum of all the scores in the distribution divided by the total number of scores (N) (the mathematical average)

When should you use median?

When distribution is strongly skewed, probably better to represent central tendency with this than mean (Pagano, 2001, p. 70) Not so useful in inferential statistics bcuz usually less stable than mean from sample to sample.

MODE

most frequent score in the distribution.

Shape of SKEWED distribution:

scores clustered on the high or low end of distribution.

Shape of ZERO SKEW is

symmetrical.

Negative skewed distribution

tail points in the NEGATIVE direction (left - think number line)

Positive skewed distribution

tail points in the POSITIVE direction (right - think of number line)

MEDIAN

the middle score of the distribution when all the scores have been ranked. if there are an even # of scores, median is average of 2 middle scores.

The mean will either _________ or _________ the center of skewed distributions.

underestimate; overestimate Think mean gravitate towards extreme scores (closer to tail)