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Central Tendency and Variability

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PSYC 210
Cathy Mc Farland

Chapter 3 – Central Tendency and Variability 1 Variable – characteristic that can have different values Score – particular person’s value on a variable Value – possible number or category that a score can have Central Tendency Central tendency – typical or most representative value of a group of scores There are three measures of central tendancy: 1. Mean 2. Mode 3. Median The Mean:  Most common measure of central tendency Mean – arithmetic average of a group of scores; sum of scores divided by the # of scores M = the mean  = the sum of X = the scores in the distribution of the variable ‘X’ N = the number of scores in the distribution M = X/N = 60/10 = 6 Steps for Getting the Mean: 1. Add up all the scores (figure out X) 2. Divide this sum by the number of scores (divide X by N) The Mode: Mode – value with the greatest frequency in a distribution; the value that is most reoccurring  In a perfectly symmetrical unimodal distribution, the mode is the same as the mean.  The mode isn’t a good way of describing the central tendency of the scores because it doesn’t reflect many aspects of the distribution. The Median: Median – middle score when all the scores in a distribution are arranged from lowest to highest 1 3 3 6 7 7 8 8 8 9 median Chapter 3 – Central Tendency and Variability 2 Steps to finding the median: 1. Line up all the scores from lowest to highest. 2. Figure how many scores there are to the middle score by adding 1 to the number of scores and dividing th by 2. Example: with 29 scores, adding 1 and dividing by 2 gives you 15. The 15 score is the middle score. If there are 50 scores, adding 1 and dividing by 2 gives you 25.5. Since there are no half scores, the 25 th and 26 scores (the scores on either side of 25.5) are the middle scores. 3. Count up to the middle score(s). if you have one middle score, this is the median. If you have two middle scores, the median is the mean of these two scores. Considering the Measures of Central Tendency:  Sometimes the median is better than the other two measures as a representative value for a group of scores. This happens when there are some extreme scores that affect the mean but wouldn’t affect the median. o Outlier – score with an extreme value (very high or low) in relation to the other scores in the distribution. Practice Questions: 1. Name and define three measures of central tendency. Mean is the average of a group of scores, sum of the scores divided by the number of scores. Median is the middle score if you were to line up the numbers from lowest to highest. Mode is the score with the highest frequency. 2. Write the formula for the mean and define each of the symbols. M = X/N M – the mean  = the sum of X = scores in the distribution of the variable ‘X’ N = the number of scores in the distribution 3. Figure the mean of the scores: 2, 3, 3, 6, and 6. 2 + 3 + 3 +6 + 6 = 20/5 = 4 4. For the following scores, find (a) the mean, (b) the mode, (c) the median: 5, 3, 2, 13, 2, and (d) why is the mean different from the median? a. M = 5 + 3 + 2 + 13 + 2 = 25/5 = 5 b. Mode = 2 c. Median = 2 2 3 5 13 d. The extreme score makes the mean higher than the median. Variability  How spread out are the scores in the distribution? This shows the amount of variability in the distribution.  How close or far from the mean are the scores in a distribution? o If the scores are quite close to the mean, then the distribution has less variability than if the scores are further from the mean. Chapter 3 – Central Tendency and Variability 3 Two measures of the variability of a group of scores: 1. Variance 2. Standard deviation 2 The Variance (SD ): Variance – measure of how spread out a set of scores are; average of the squared deviations from the mean  The average of each score’s squared difference from the mean Steps to find the variance: 1. Subtract the mean from each score. This gives each score’s deviation score, which is how far away the
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