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Chapter 3: Central Tendency - Coggle Diagram
Chapter 3: Central Tendency
Central tendency
is known as being a statistical measure to determine a single score that defines the center of a distribution.
The goal of central tendency is to find the single score that is most typical or most representative of the entire group.
In addition to describing an entire distribution, measures of central tendency are also useful for making comparisons between groups of individuals or between sets of data.
In everyday language, central tendency attempts to identify the “average” or “typical” individual.
The second measure of central tendency we will consider is called the median.
If the scores in a distribution are listed in order from smallest to largest, the median is the midpoint of the list.
Defining the median as the midpoint of a distribution means that that the scores are being divided into two equal-sized groups
Median is the midpoint of the list. More specifically, the median is the point on the measurement scale below which 50% of the scores in the distribution are located.
Mean
also referred to as the arithmetic average, is computed by adding all the scores in the distribution and dividing by the number of scores.
The formula for population mean is computed by adding all the scores in the population, and then dividing by N.
μ = (ΣX)/ N
N = the number of items in the group.
X = all the individual items in the group.
Σ means “the sum of.”
Like population mean but a little different, sample mean is identified with the symbol M. Once we see this we should realize that we are dealing with a sample. Also the formula for the sample mean uses a lowercase n as the symbol for the number of scores in the sample.
n means “the number of items in the sample”
M means "sample mean"
M=( ΣX) / n
The mean for a population is identified by the Greek letter mu,
(μ)
Many time is is necessary to combine two sets of scores and then find the overall mean for the combined group.
The overall sum of the scores for the combined group
The total number of scores in the combined group
To calculate the overall mean, we need two values:
The final measure of central tendency is called the mode.
Mode is a useful measure of central tendency because it can be used to determine the typical or most frequent value for any scale of measurement, including a nominal scale
A distribution with two modes is bimodal,
There are no symbols or special notation used to identify the mode or to differentiate between a sample mode and a population mode.
A distribution with more than two modes is called multimodal.
In a frequency distribution, the mode is the score or category that has the greatest frequency.
Symmetrical Distributions
Symmetrical distribution, the right-hand side of the graph is a mirror image of the left-hand side.
If a distribution is perfectly symmetrical, the median is exactly at the center because exactly half of the area in the graph will be on either side of the center.
