Chapter 3

For a positively skewed distribution with a mode of and a median of , what is the most likely value for the mean? A. Greater than 25 B. Less than 20 C. Between 20 and 25 D. Cannot be determined by the information given

A

Multimodel

A distribution with more than two modes

Where is median found in a skewed distribution?

Toward the long tail, but not as far as the mean

Bimodel

a distribution with two modes

Characteristics of the Mean

- Changing the value of score changes the mean - Introducing new score or removing score changes mean, unless score added or removed is EXACTLY equal to mean - Adding or subtracting constant from each score changes mean by same constant - Multiplying or dividing each score constant multiplies or divides mean by that constant

Median

- Midpoint of the scores when listed from smallest to largest - Divides scores into 2 groups of equal sizes

Mode

- Score/category that has greatest frequency - You can have more than one mode ---> In a graph, if there is more than one mode, they have have two peaks that are equal peaks

Mean

- The sum of all the scored divided by # of scores in data - arithmetic average - 2nd way of describing mean as a balance point

T/F 1. The mean uses all of the scores in the data, so it is the best measure of central tendency for skewed data. 2. If the mean and median have the same values, the distribution is probably symmetrical.

1. False; the mean will be moved toward the long tail in skewed data so it may not be at all representative of the "middle" 2. True; when mean and median are the same, distribution HAS to be symmetrical

T/F 1. It is possible for more than 50% of the scores in a distribution to have values above the mean. 2. It is possible for more than 50% of the scores in a distribution to have values above the median.

1. True; more than 50% of the scores in a negatively skewed distribution will be above the mean 2. False; median defined as score that divides distribution exactly in half- 50% above/below

The Weighted Mean

3 steps: - Determine combined sum of all scores - Determine combined number of scores - Divide sum of scores by total number of scores

Central Tendency

A statistical measure to determine a single score that defines the center of a distribution The goal of this is to find single score that is the best to represent the entire group

A distribution of scores shows mean= 31 and median= 43. The distribution is probably A. Positively Skewed B. Negatively Skewed C. Bimodel D. Open-ended

B

Where is the mean located if it is influenced by extreme scores?

Found far toward the long tail (positive or negative skewed)

For a negatively skewed distribution, what is the most probable order for the three measures of central tendency from smallest to largest?

Mean, median, mode

What is the best measure of central tendency for an extremely skewed distribution of scores?

Median

Where is the mode found?

Near the short tail

What is the distribution if the mean-median < 0?

Negatively Skewed

Can there be a mode if a distribution have many equally high peaks?

No

What is the distribution if the mean-median > 0?

Positively Skewed