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Chapter 4

Chapter Four PSY201

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Kristie Dukewich

Chapter Four: Measures of Central Tendency and Variability – to quantify the distributions + computing the average score for each group and then comparing the averages + measure of the central tendency of each distribution – variability + specifies the extent to which scores are different from each other, are dispersed, or spread out + important for two reasons: - 1. determining the variability of the data is required by many of the statistical inference tests - 2. variability of a distribution can be useful in its own right - average value of scores and how variable the scores are - variability of scores is important because need to know whether the effect varies or is in uniform – central tendency and variability are the two characteristics of distributions that are most often quantified – arithmetic mean is the sum of the of the scores divided by the number of scores Properties of the mean – the mean is sensitive to the exact value of all the scores in the distribution – to calculate it, you have to add all the scores, so a change in any of the scores will cause a change in the mean – not true of median/mode – the sum of the deviations about the mean equals zero – if the mean is subtracted from each score, the sum of the differences will equal zero ;; mean is the balance point of the distribution – the mean is very sensitive to extreme scores – if we added an extreme score (one far from the mean), it would greatly disrupt the balance + the mean would have to shift a considerable distance to reestablish balance + mean is more sensitive to extreme scores than is the median or the mode – the sum of the squared deviations of all the scores about their mean is a minimum. ^ is a minimum + this property states that although the sum of the squared deviations about the mean does not usually equal zero, it's smaller than if the squared deviations were taken about any other value – Under most circumstances, of the measures used for central tendency, the mean is least subject to sampling variation + if repeatedly take samples from a population on a random basis, mean would vary from sample to sample – same for median and the mode + median varies less than others The Overall Mean – know the mean of several groups of scores and want to calculate the mean of all the scores combined - overall mean is equal to the sum of the mean of each group times the number of scores in the group, divided by the sum of the number of scores in each group + the overall mean really is a weighted mean where the weights are the number of scores used in determining each mean The Median – symbol Mdn + defined as the scale value below which 50% of the scores fall + same thing as P50. – when dealing with raw (ungrouped) scores, it's easy to find the median + first, arrange scores in rank order + the median is the centermost score if the number of scores is odd. If the number is even, the median is taken as the average of the two centermost scores + rank the order from lowest to highest + the middle number would be P50 – if the number of scores is even, the median is the average of the two centermost scores + add then divide the two numbers by two – if there's three of the same numbers near the middle... + if the median occurs at a value where there are tied scores, then use the tied scores as the median Properties of the Median – the median is less sensitive than the mean to extreme scores – ie: the last score is drastically different to each one + mean is drastically different + median stays the same – not responsive to each individual score but rather divides the distribution in half, it is not sensitive to the extreme scores as is the mean → when distribution is strongly skewed, it's better to represent the central tendency with the median rather than the mean – involves its sampling stability + under usual circumstances, the median is more subject to sampling variability than the m
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