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UofL PSYC 301 - Central Tendency & Variability
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PSYC 301 1st Edition Lecture 2CENTRAL TENDENCY & VARIABILITYOutline of Last Lecture I. Different types of VariablesII. Presenting data in graphsIII. Distributing dataOutline of Current Lecture II. Characterize the center of a distribution of dataIII. Calculate how much scores varyCurrent LectureI. SUMMARIZING THE DATA (STEPS)1) Find out the shape of the distribution (Make a histogram)2) Quantify the center of the distribution (mean, median, mode)3) Quanitify the spread of the distribution (Range, standard deviation, variance)II. SUMMARIZING THE CENTER: (Central Tendencies – mean, median, mode, range)a. MEANi. The average: add up all scores and divide by n. (the number of scores)b. MEDIANi. The middle of the data set when arranged from lowest to highest- If data set has an even number of data points, you take theaverage of the 2 numbers closest to the middlec. MODEi. Most frequently observed data point (may by more than one number)d. RANGEi. The largest value minus the smallest valueIII. SUMMERIZING THE DATA : CENTERa. A distribution of data can only have 1 meanb. A distribution of data can only have 1 medianc. A distribution of data can have many modes, up to the number of n’sd. The mean is most appropriate for interval datae. The median can be applied to ordinal or interval dataf. The mode can be applied to interval, ordinal, or nominal datag. In a histogram, when data are symmetric and unimodal, the mean, median, and mode are very close to one another at the center.These notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.h. In a histogram, when distributions are skewed, the mean, median, and mode spread outi. Means are strongly affected by outliers, the medians and modes are not. j. Sometimes the means don’t tell the whole story. You could have one data set where everyone’s scores were within a range of 3, and one set where the scores have a range of 13, with the means being the sameIV. SUMMARIZING THE DATA: SPREADa. Standard Deviation (SD) measures the average deviation from the mean value- “average”: add something up and divide by n- “deviation”: (difference) subtract two numbers- “deviation from the mean”: subtract scores minus the mean- x: one data point- : the mean of the data points- : the sum- n: the total number of scores (x)ii. the deviation is squared because if you didn’t square the deviation from the mean, you would always end up with a sum of zeroiii. the square root undoes the squared deviationSTEPS:1) calculate the mean2) take each score and subtract the mean3) square each deviation4) add all deviations up5) divide by n6) take the square root EXAMPLE: x = [2 4 8 10]1) calculate the mean 2+4+8+10= 2424/n (n=4) → 24/4= 6 The mean is 62) Calculate the deviations from the mean: ( x - ) ( 2 – 6 ) = - 4( 4 – 6 ) = - 2( 8 – 6 ) = 2( 10 – 6 ) = 43) Square each deviation: ( x - ) ² -4 ² = 16-2 ² = 42 ² = 44 ² = 164) Add up all deviations 16 + 4 + 4 + 16 = 40SS = 405) Divide SS byn 40 / 4 = 106) Take the square root √10 = 3.16SD = 3.16b. Variance measures the average squared deviation from the mean value. (Larger deviations indicate greater spread.)- Variance has the same steps as SD, except taking the square root in step 6.- ( √var = SD / SD² = Var )- x: one data point- : the mean of the data points- : the sum- n: the total number of scores (x)STEPS:1) calculate the mean2) take each score and subtract the mean3) square each deviation4) add all deviations up5) divide by n6) take the square root EXAMPLE: x = [3 5 8 12]1)calculate the mean 3 + 5 + 8 + 12 = 2828/n (n=4) → 28/4= 7The mean is 72) Calculate the deviations from the mean: ( x - ) ( 3 – 7 ) = - 4( 5 – 7 ) = - 2( 8 – 7 ) = 1( 12 – 7 ) = 53) Square each deviation: ( x - ) ²-4 ² = 16-2 ² = 41 ² = 15 ² = 254) Add up all deviations 16 + 4 + 1 + 25 = 46SS = 465) Divide SS byn 46 / 4 = 11.5Variance = 11.5QUESTIONS:- Which measure(s) of central tendency is/are robust to outliers?- Median & mode- Which measure of center should you use if your data are skewed?- Median- What is the relationship between standard deviation and variance?- Variance is standard deviation


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UofL PSYC 301 - Central Tendency & Variability

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