PSY 302: Chapter 3 Textbook Notes
PSY 302: Chapter 3 Textbook Notes PSY 302
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Date Created: 10/12/15
CHAPTER 3 Measures of Central Tendency Central Tendency The value typically in the middle that is most representative of a set of scores Attempts to identify the most average individual quotNumber Crunching term used when statisticians condense a set of scores down to the central tendency There39s no single standard procedure for measuring central tendency No single measure produces a central representative value in every situation The three distribution methods show that A The first is symmetrical it meets in the middle central tendency is easy to identify B In a negatively skewed distribution the peak of the graph is not the central tendency It is defined by a value smaller than the peak C The third is confusing because there are two piles It seems like there should be two midpoints For these complex kinds of scales statisticians have come up with the concepts mean median and mode 393 b I r IQSJE BOX 123456780x C f 1213456789X The Mean 0 Mean The average Adding all scores together and then dividing that by the amount of scores The mean for a population is identified by the Greek letter mu and for a sample it39s with M or lt or xbar Think of it as the amount an individual would get if the scores were divided evenly The formula for a populationsample mean is I MuM SigmaXN O The Weighted Mean It is sometimes necessary to combine two sets of scores to find the overall mean for a group Say we have a sample of n12 M6 and a sample of n8 M7 To figure this out we add both ns together to get 20 and we add both sample sums together then divide the sum by n To get the sample sums here we multiply M by n So here the sample sums are 72 and 56 128 O O 39 12820 64 The weighted mean is 64 Computing Mean From A Frequency Distribution Table When using the table make sure you take the frequency of each score into account Characteristics of the Mean Adding a score always changes the mean except when that score is the exact same as the mean Adding and Subtracting Constants from the Score If a constant value is added tosubtracted from every score in a distribution the same constant value is added to the mean Dividing and Multiplying Each Score by a Constant If a constant value is used to multiply and divide every score in a distribution the mean changes in the same way It39s a common way of changing units of measurement in data The Median The midpoint of a distribution that is ordered from smallest to largest it39s the point 50 of the scores are below When the amount of scores the median is determined from is even the midpoint between the two central scores is the median Finding The Precise Median ForA Continuous Variable O The precise median is the point where the bottom 50 and the top 50 are separated perfectly In a discrete variable the median has to be a whole number but with a continuous variable something with a median of 4 might actually have a median anywhere between 35 and 45 Discrete variables do not have a precise median for this reason Say we have this distribution O b 4 4 I 3 gt Ed L1 3 83 G 2 32 Q 1 1 4567X 012345 Meclldn 375 39 We can see that the median is 4 However to get the precise median we have to find a fraction of the boxes on the histogram that would make one box with this 0 Fraction needed number needed to reach 50number in the interval 0 We need one more box to reach four boxes and there are four boxes in the interval So we need 14 of each box to make one box 0 We then add 14 to the bottom of the interval in this case it39s 35 because the median is 4 but we need to take real limits into account The precise mean is 375 The Mode 0 The most common observation among a group of scores it39s seen the most 0 The mode is the only measure of central tendency that can be used with nominal data 0 Bimodal two modes 0 Multimodal more than two modes Sometimes two modes in a study aren39t equal ie one has 7 scores and the other has 8 The larger mode is the major mode and the smaller is the minor mode Selecting a Measure of Central Tendency O The mean is typically preferred with numerical data since it uses every score in the data 0 The median is better when 0 There are a few extreme scores in a data set they can severely skew the mean 0 There is an undetermined score ie participants are given a task and one participant does not finish in the allotted time 0 There is an open ended distribution e an option in the study is quot5 or morequot That39s open ended 0 There is ordinal data 0 The mode is better when 0 There is nominal data 0 The variables are discrete ie why would you calculate the mean for something like the number of rooms in a house 0 Describing shape the mode is often used as a supplement to the mean to help get a better understanding of what a set of data looks like Line Graph Used to show separate means medians or other statistics through dots connected by lines Histograms can also be used for this Median is sometimes abbreviated as mdn Central Tendency and Shape of the Distribution 0 Symmetrical The mean mode and median are either the same in a perfectly symmetrical graph or close in a roughly symmetrical graph If a symmetrical graph has two modes then the median and mean are only identical 0 Skewed Positive The mode is to the left followed by the median and mean Negative The mean is to the left followed by the median and mode
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