Measures of Central Tendency
A way to summarize a variable is to identify
the most “typical” score.
Measures of Central Tendency are different
“typical” scores and represent values
around which others concentrate.
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Measures of Central Tendency & Variability: Mode, Median, Mean, Range, Variance, Deviation, Lecture notes of Social Statistics and Data Analysis
An overview of measures of central tendency, including the mode, median, and mean, as well as measures of variability such as range, variance, and standard deviation. It also discusses the importance of the normal distribution and z-scores in statistics, and covers topics such as statistical estimation, confidence intervals, hypothesis testing using t-tests, anova, and chi-square.
Typology: Lecture notes
2011/2012
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Measures of Central Tendency
A way to summarize a variable is to identify
the most “typical” score.
Measures of Central Tendency are different
“typical” scores and represent values
around which others concentrate.
The Mode
The mode is the value with the highest
frequency count.
While the mode can be useful, it is very
informative as it only tells us which value
occurred the most frequently.
The Mean
The mean incorporates all of the values for a variable! Called the “average”, it is obtained by adding up all the values & dividing that sum by the total number of cases.
Usually the most accurate, stable and useful measure of central tendency….it is vulnerable to distortions by extremely high or low values.
Measures of variability
A quick measure of variability is the range. To calculate the range ( R ) you subtract the lowest value ( L ) for a variable from the highest value ( H ).
Although better than nothing, it is based only on the two most extreme variable scores….and ignores all the other information about the dispersion in the data.
The variance reflects the sum of deviations of each value from the mean and provide us with an “average” amount of dispersion or variability. The standard deviation is the square root of the variance.
From descriptive to inferential statistics….
The “normal distribution” and z -scores connect descriptive statistics to inferential statistics.
The ND adds to the interpretation of the mean and standard deviation, and is the basis for statistical estimation, hypothesis testing, and measures of association.
Key aspects of the normal curve:
The normal curve is symmetrical or bell-shaped.
The mean is also the most frequently occurring value (the mode), and the value that splits the distribution in half (the median).
Assuming a variable is normally distributed in the population, we can say much more about the standard deviation.