Chapter 3 Measures Of Central Tendency

Open-Ended

A distribution is said to be ____-_____ when there is no upper limit (or lower limit) for one of the categories

Multimodal

A distribution with more than two modes is called __________

Bimodal

A distribution with two modes is said to be _______

Mean

Also known as the arithmetic average, is computed by adding all the scores in the distribution and dividing by the number of scores. The ____ for a distribution is the sum of the scores divided by the number of scores

Continuous Variable

Can be infinitely divided

Positively Skewed

Distribution with the peak (highest frequency) on the left-hand side; this is the position of the mode; The vertical line drawn at the mode does not divide the distribution into two equal parts; the median must be located to the right of the mode; the mean is located to the right of the median because it is the measure of central tendency that is influenced most by the extreme scores in the tail and tends to be displaced toward the tail of the distribution; the typical order of the three measures of central tendency from smallest to largest (left to right) is the mode, median, and the mean.

Negatively Skewed

Distributions are lopsided in the opposite direction, with the scores piling up on the right-hand side and the tail tapering off to the left. The mode is on the right-hand side (with the peak); The mean is displaced toward the left by the extreme scores in the tail; The median is usually located between the mean and the mode. The most probable order for the three measures of central tendency from smallest value to largest value (left to right) is the mean, median, and the mode

Skewed Distribution

Especially distributions for continuous variables, there is a strong tendency for the mean, median, and mode to be located in predictably different positions

Median

If the scores in a distribution are listed in order from smallest to largest, the ______ is the midpoint of the list. More specifically, the ______ is the point on the measurement scale below which 50% of the scores in the distribution are located

Mode

In a frequency distribution, the ____ is the score or category that has the greatest frequency

Central Tendency

Is a statistical measure that attempts to determine the single value, usually located in the center of a distribution, that is most typical or most representative of the entire set of scores

Precise Median

Is located in the interval defined by the real limits of the value

Mean

Is the balance point of a distribution; defined by distances; often is not the midpoint of the scores

Median

Is the midpoint of a distribution; defined by number of scores; often is not the balance point of the scores

Line Graph

Is used when the values on the horizontal axis are measured on an interval or a ratio scale. An alternative to the line graph is a histogram

Middle

Mean & Median; measure central tendency; using two different concepts of "Middle"

Weighted Mean

Often it is necessary to combine two sets of scores and then find the overall mean for the combined group. to calculate the overall mean, we need two values: (1) the overall sum of the scores for the combined group and (2) the total number of scores in the combined group. Because the samples are not the same size, one makes a larger contribution to the total group and therefore, carries more weight in determining the overall mean. For this reason, the overall mean we have calculated is the ________ mean

Negatively Skewed Distribution

Problems begin to appear. Now the scores form a __________ skewed distribution, piling up at the high end of the scale and tapering off to the left all the way down

Number Crunching

Statisticians sometimes use the expression ______ crunching to illustrate this aspect of data description. That is, we take a distribution consisting of many scores and "crunch" them down to a single value that describes them all

Population Mean

The mean for a population is identified by the Greek letter mu, μ (pronounced "mew")

Sample Mean

The mean for a sample is identified by M or x̄ (read x-bar). If a mean is identified with the symbol M, you should realize that we are dealing with a sample. The equation for the sample mean uses a lowercase n as the symbol for the number of scores in the sample

Symmetrical Distribution

The right hand side of the graph is a mirror image of the left-hand side; the median is exactly at the center because exactly half of the area in the graph is on either side of the center; the mean also is exactly at the center because each score on the left side of the distribution is balanced by a corresponding score (the mirror image) on the right side; the mean (balance point) is located at the center of the distribution; Thus for a perfectly symmetrical distribution, the mean and the median are the same

The mean as a balance point

The second alternative definition of the mean describes the mean as a balance point for the distribution. If the seesaw is positioned so that it pivots at a point equal to the mean, then i will be balanced and will rest level. The reason that the seesaw is balanced over the mean becomes clear when we measure the distance of each box (score) from the mean. The mean balances the distances. That is, the total distance below the mean is the same as the total distance above the mean. Because the mean serves as a balance point, the value of the mean is always located somewhere between the highest score and the lowest score; the mean can never be outside the range of scores.

Dividing the total equally

the first alternative is to think of the mean as the amount each individual receives when the total (ΣX) is divided equally among all of the individuals (N) in the distribution. This somewhat socialistic viewpoint is particularly useful in problems for which you know the mean and must find the total

Minor Mode

the shorter peak is the _____ mode

Major Mode

when two modes have unequal frequencies, researchers occasionally differentiate the two values by calling the taller peak the _____ mode