A Very Brief Introduction to Some (Social Science) Statistics
Depending on your age, you might remember when addition, subtraction, multiplication and division was all the buzz; or maybe for your generation it was or is algebra, geometry or trigonometry. Not necessarily the newest, but one of the more technological ways of finding an average these days is through the means of statistics; and that's what this article/paper is about.
For those of us who have studied in the social sciences, you're most likely familiar with hearing and learning about averages and probably already know a little something about statistics. For those of you who are not too or at all familiar with computing averages, this paper can be seen as a very rudimentary introduction to social science statistics for you. All-in-all, you're likely to come away at least a little informed and knowledgeable in the statistical aspect of social sciences.
Measuring Central Tendency
The name in itself is self-explanatory. Central is what is in the center, the middle of something. When something is central it's at the half way point. There's half in front and half behind of what is in the middle (center). The arithmetic mean is the most commonly used measure of central tendency.
Take the number 11, for instance. The number 6 would be the arithmetic mean, also known as just mean, because it's in the middle. They are exactly 5 numbers in front of and behind the number 6. So the number 6 is half way from the number 1, but also half way to the number 11. So, for this equation, 6 is the number that we're looking for.
The Median
The median, which is the defined as the middle score in a tendency; is another commonly used method of measuring central tendency. The median is used by looking at a set of scores in ascending and descending order, for instance.
Say that 100 point test was given to a class and the scores were 100, 85, 80, 70, 60, 50, 30, 15 and 10. The median score would be arrived at by taking the number in the exact middle of the 9 set of numbers of an odd number, which would give you the median. The number right in the middle is 60, so 60 is the median. They're exactly 4 numbers before and after the number 60, so 60 is in the exact middle, thus our median.
When there are an even number of ascending and descending numbers or numbers in a row, the two middle numbers are added and divided to arrive at the median. So, if someone had scored a 5 on the test also, that would give us 10 numbers, not 9, an even number, not odd number; therefore you would add the numbers 60 and 50 together and divide by 2 and get the number 55, the median.
The Mode and Bimodal
The mode is the score that occurs the most frequently in a distribution of scores. Take for instance the scores 43 34 45 51 42 31 51. The score 51 appears twice, more than any of the other scores, therefore 51 is the mode in these scores. When two scores appear with the highest frequency, it's said to be bimodal. So, if any of these other scores had appeared as frequently as 51, they would be a mode also, thus there would be two modes, making the mode bimodal.
Measures of Variability
Variability is a way in which scores in a distribution are dispersed or scattered. For example, more than one distribution of test scores can have the same mean, but the test scores can be distributed differently around the mean. Take for examples, distributions on tests A and B in which both the mean scores were 50, but for test A the scores were widely distributed around the mean; whereas for test B, not many of the scores varied too much from higher than 60 to lower than 40.
The Range
The range is the difference between the highest number or score to the lowest number or score in a sequence of scores or numbers. So, if we go back to our example from Mode and Bimodal, the lowest score was 31, and the highest score was 51, giving a difference of 20. Thus the range between those numbers is 20. Thus those numbers' range is from 31 to 51.
The Standard Deviation
The standard deviation is the measure of variability that is equal to square root of the average squared deviations about the mean. To be more specific, it's equal to the square root of the variance. And the variance is equal to the arithmetic mean of the squares of the differences in a distribution and mean of that distribution. Variances are commonly used in psychological research.
Skewness
Skewness is what characterizes a distribution based on the nature and extent to which symmetry is or isn't present. A distribution can have a positive skew, though skewness in itself is neither good or bad, normal or abnormal. A positive skew is when few scores of scores fall at the higher end of a distribution.
Whereas it might have been thought before that statistics are just for scientists and social scientists and used in labs for research; the use of statistics are becoming more and more-so a common place and important part of our everyday routines. Some basic statistics can be helpful and useful in helping the average individual to figure out and better arrive at some problem solving and mathematical equations that he or she may not have been able to have comprehended without such knowledge.
Reference
Ronald Jay Cohen & Mark E. Swerdlik. Illinois State University. Psychological Testing and Assessment: An Introduction to Tests and Measurement. Sixth Edition. McGraw-Hill Education (Asia) and Posts & Telecom Press. 2005.
How helpful did you find this article/information in helping you to learn and/or comprehend statistics for the social sciences?
Measuring Central Tendency
The name in itself is self-explanatory. Central is what is in the center, the middle of something. When something is central it's at the half way point. There's half in front and half behind of what is in the middle (center). The arithmetic mean is the most commonly used measure of central tendency.
Take the number 11, for instance. The number 6 would be the arithmetic mean, also known as just mean, because it's in the middle. They are exactly 5 numbers in front of and behind the number 6. So the number 6 is half way from the number 1, but also half way to the number 11. So, for this equation, 6 is the number that we're looking for.
The Median
The median, which is the defined as the middle score in a tendency; is another commonly used method of measuring central tendency. The median is used by looking at a set of scores in ascending and descending order, for instance.
Say that 100 point test was given to a class and the scores were 100, 85, 80, 70, 60, 50, 30, 15 and 10. The median score would be arrived at by taking the number in the exact middle of the 9 set of numbers of an odd number, which would give you the median. The number right in the middle is 60, so 60 is the median. They're exactly 4 numbers before and after the number 60, so 60 is in the exact middle, thus our median.
When there are an even number of ascending and descending numbers or numbers in a row, the two middle numbers are added and divided to arrive at the median. So, if someone had scored a 5 on the test also, that would give us 10 numbers, not 9, an even number, not odd number; therefore you would add the numbers 60 and 50 together and divide by 2 and get the number 55, the median.
The Mode and Bimodal
The mode is the score that occurs the most frequently in a distribution of scores. Take for instance the scores 43 34 45 51 42 31 51. The score 51 appears twice, more than any of the other scores, therefore 51 is the mode in these scores. When two scores appear with the highest frequency, it's said to be bimodal. So, if any of these other scores had appeared as frequently as 51, they would be a mode also, thus there would be two modes, making the mode bimodal.
Measures of Variability
Variability is a way in which scores in a distribution are dispersed or scattered. For example, more than one distribution of test scores can have the same mean, but the test scores can be distributed differently around the mean. Take for examples, distributions on tests A and B in which both the mean scores were 50, but for test A the scores were widely distributed around the mean; whereas for test B, not many of the scores varied too much from higher than 60 to lower than 40.
The Range
The range is the difference between the highest number or score to the lowest number or score in a sequence of scores or numbers. So, if we go back to our example from Mode and Bimodal, the lowest score was 31, and the highest score was 51, giving a difference of 20. Thus the range between those numbers is 20. Thus those numbers' range is from 31 to 51.
The Standard Deviation
The standard deviation is the measure of variability that is equal to square root of the average squared deviations about the mean. To be more specific, it's equal to the square root of the variance. And the variance is equal to the arithmetic mean of the squares of the differences in a distribution and mean of that distribution. Variances are commonly used in psychological research.
Skewness
Skewness is what characterizes a distribution based on the nature and extent to which symmetry is or isn't present. A distribution can have a positive skew, though skewness in itself is neither good or bad, normal or abnormal. A positive skew is when few scores of scores fall at the higher end of a distribution.
Whereas it might have been thought before that statistics are just for scientists and social scientists and used in labs for research; the use of statistics are becoming more and more-so a common place and important part of our everyday routines. Some basic statistics can be helpful and useful in helping the average individual to figure out and better arrive at some problem solving and mathematical equations that he or she may not have been able to have comprehended without such knowledge.
Reference
Ronald Jay Cohen & Mark E. Swerdlik. Illinois State University. Psychological Testing and Assessment: An Introduction to Tests and Measurement. Sixth Edition. McGraw-Hill Education (Asia) and Posts & Telecom Press. 2005.
How helpful did you find this article/information in helping you to learn and/or comprehend statistics for the social sciences?
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