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29 Cards in this Set

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  • Back
What is meant by the variability of a set of scores?
Refers to how spread out or scattered teh scores in a distribution are.
Why is it usually essential to know about the variability of a set of scores, rather than just the central tendency? For example, how might your grade on a midterm exam be strongly affected by the variability of teh examination scores?
The central tendency just shows where the average scores far but does not take into acount what scores mean when they are distance from the mean. 10pts from the mean can be a great distance or no difference at all.
What is the range, and how is computed?
The range is the largest score minus the lowest score.
Why is the range ussually not used as the measure of variability?
It does not tell us enough information about the data, where the data fell, what the data means.
What are the interquartile and semi-interquartile ranges?
the interquartile range is the middle 50% of the socres, the semi-interquartile range is the middle 25% of the scores
How are these measures computed, and when should they be used?
For IQR Calculate the 75th percentile, the 25th and the median. The range between 25th and 75th is the IQR. For the SIQR take the 75th minus 25th and divide by 2.
Why can't we use the average of the deviation scores as a measure of variability? How does squaring all of the deviations solve this problem?
Because it would equal zero, by summing the deviation of the average it causes for all scores to be positve thus allowing to measure the average
Whtat is the sum of squares of a set of scores?
The variance
What is the standarad deviation of a set of scores? What advantage does the standard deviation have over the variance as a measure of variability?
The sq root of the variance, it is better because of its properties in a normal distribution
When computing the variance or standard deviation, when should the sum of the squared deviations be divided by N? When should you divide instead by N - 1?
When it is a statistic the square of deviations should be divided by N. When it is a parameter it should be divided by N-1.
Why is it usually easier to calculate the value of the variance or standard deviation by using the computing formulas?
Because it will yeild more answers with decimal places.
What are some of the useful mathematical properties of the standard deviation?
Its based on all scores in the data and describes the data
Why might the mean and standard deviation not be a good way to summarize a particular set of data?
It is only good for information that is symetric and has one mode
What is a five-number summary, how is it constructed, and what kinds of information does it provide?
The mean is at the top, the first and third quartile scores and the lowest and highest score.
What is a box-and-whisker plot particularly useful?
When there is skewed data and you want to compare to different sets of data
For what kinds of data are box-and-whisker plots particularly useful?
Data that is used to compare
What is a mean-on-spoke representation, and how is it constructed?
A mean and spoke is useful for normally distributed data. You take the Mean and put a dot and then draw spokes 1SD above and below the mean.
For what kinds of data are mean-on-spoke representations preferable to box-and-whisker plots?
Normally distributed data.
What is the advantage of using a transformed score, such as a percentile rank?
To make data that can be compared to other sets of data.
When comparing two (or more) scores from different distributions, why is it necessary to refer each score to its mean and standard deviation? What errors are we likely to make if we look only at the raw scores?
You need to look at mean and SD but you do not know what the score means in relation to the rest of the data. Also by comparing raw data you do not not what score was actually higher on which test.
What will happen to the mean and standard deviation of a set of scores if we do the following: Add a constant to every score? Subtract a constant from every score? Multiply every score by a constant? Divide every score by a constant?
Addition: Mean will have constant added, no difference in SD. Subtract: Vice-versa of Addition. Multiply and Divide: The SD and Mean will both be affected by the k.
How can these rules be used to obtain transformed scores with any desired mean and standard deviation?
You can add or subtract the mean to make the score seem greater than it actually it is.
What is the mean and standard deviation of a set of z scores? Why is this desirable?
The mean of z scores is 0 and the SD is 1.0
How are z scores computed?
You take the the score, subtract the mean and divide by the SD
When raw scores are transformed into z scores, what happens to the shape of the distribution?
The distribution becomes normal.
Why might we prefer to use T scores or SAT scores instead of z scores?
So someone not versed in statistics would understand the data
How are T scores and SAT scores computed?
You multiply z by 10 for the standard deviation and add 50 to creat a mean of 50.
What is the mean and standard deviation of set of T scores or a set of SAT scores?
T = Mean is 50 and SD is 10
SAT = Mean is 500 and SD is 100
What is the mean and standard deviation of a set of IQ scores, and how are these scores computed?
IQ = Mean is 100 and SD is 15. By transforming z scores into the formula.