o Count, frequency, percent
o Shows how often something occurs
o Use this when you want to show how often a response is given
Measures of Frequency
o Range, Variance, Standard Deviation
o Identifies the spread of scores (intervals)
o Use this when you want to show how “spread out” the data are
o It is helpful to know when your data are so spread out that it affects the mean
Measures of Dispersion or Variation
o Mean, Median, and Mode
o Locates the distribution by various points
o Use this when you want to show how an average or most commonly indicated response
Measures of Central Tendency
o Percentile Ranks, Quartile Ranks
o Describes how scores fall in relation to one another (standardized scores)
o Use this when you need to compare scores to a normalized score (e.g., a national norm)
Measures of Position
Statistical measure to determine a single score that defines the center of the distribution.
Usually attempts to identify the “average” or “typical” individual
Useful for making comparisons between groups of individuals or between sets of data
Measures of Central Tendency
- Easily understood - Not a distant mathematical abstraction
- Objective and rigidly defined - Should encounter no question as to what the value is
- Stable - Not affected materially by minor variations in the groups of items
- Easily amenable to further statistical computation
Characteristics of a Good Average
Arithmetic average
Computed by adding all the scores in the distribution and dividing by the number of scores
The Mean
a modification of the usual mean that assigns weights (or measures of relative importance) to the observations to be averaged.
The Weighted Mean
which of the statements are true or are they both true or false
i) The sum of the deviations of the values from the mean is zero.
ii) The sum of the squared deviations is minimum when the deviations are taken from the
mean
both statements are true
The positional middle of the arrayed data
In an array, one-half of the values precede the _____and one-half follow it
Definition and computations for a sample and for a population are the identical
The Median
which of the statements are true or are the both true or false
- The median is a positional measure.
- The median is affected by the position of each item in the series but not by the value of each
item. This means that extreme values affect the median less than the arithmetic mean.
both are true
The observed value that occurs most frequently
Locates the point where the observation values occur with the greatest density
The Mode
which of the statements about mode are true or are both true or false
- It does not always exist; and if it does, it may not be unique. A Data Set is said to be unimodal if
there is only one mode, bimodal if there are two modes, trimodal if there are three modes, and
so on. - It is not affected by extreme values.
- The mode can be used for qualitative as well as quantitative data.
both statements are true
What is the correct measure of central tendency to use for the following?
Extreme scores or skewed distributions
Undetermined values
Open-ended distributions
Ordinal scales
Median
What is the correct measure of central tendency to use for the following?
Nominal scales
Discrete variables
Describing shape
Mode
