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1 Sociology 301 Exam Review Liying Luo Exam Review: Logistics Exams must be taken at the scheduled date and time unless 1. You provide verifiable documents of unforeseen illness or family emergency, or notify ME in advance of religious observance or mandatory Universitysponsored event that precludes your taking the exam; AND 2. You arrange with ME to schedule a make-up date and time. Exam Review: Logistics Each exam covers lectures from since the previous exam and up to the exam date. Questions will consist of a mix of short answers and computational problems. semi-open note exams ONE sheet of paper with formulas, definitions, and other information, written on both sides. Write your name at the top of this sheet, enclose it inside your exam booklet, and turn them in at the end of the exam period.

2 Exam Review: Logistics Don t forget to bring your calculator! Exam Review: Overview measure of central tendency measure of dispersion percentile and standardized score probability and normal distribution Exam Review: Measure of Central Tendency measures of central tendency mean, mode, and median Make sure you are able to identify/compute mean, mode, and median. interpret mean, mode, and median.

3 Exam Review: Measure of Central Tendency mode: the value(s) that appear(s) most often A variable can have more than one mode. mean: Exam Review: Measure of Central Tendency median: the value(s) that appears exactly half of all observations fall above that point and half fall below that point. the value at which the cumulative percentage reaches 50%. Exam Review: Measure of Central Tendency to compute median for a continuous variable: (1) arrange the observations in order of size from lowest to highest; (2) if N (the number of observations) is odd, then the median is the middle observation; (3) if N is even, then the median is the mean of the middle two observations.

4 Exam Review: Measure of Central Tendency to compute median for a discrete variable: (1) arrange the categories from lowest to highest; (2) construct a cumulative percentage distribution; (3) identify the lowest category whose cumulative percentage equals or exceeds 50%. Exam Review: Measure of Central Tendency best measure of central tendency to describe household income? mean, median, and mode for discrete variables? nominal variables: mean, median, and mode ordinal: mean, median, mode the influence of outliers on mean, median, and mode Exam Review: Measure of Dispersion measures of dispersion range variance & standard deviation Make sure you are able to calculate appropriate measures of dispersion for different type of variables. interpret these measures.

5 Exam Review: Measure of Dispersion range: the difference between the largest and the smallest observation three steps to compute the range: 1. Rewrite/sort the values from lowest to highest; 2. Identify the minimum and maximum values; 3. Calculate the range: range = maximum value minimum value Exam Review: Measure of Dispersion Unlike the range, two measures of dispersion describe how all observations are spread in relation to the mean. variance: the mean (average) squared difference between each observation and their mean s Y 2 = (Y 1 Y) 2 + (Y 2 Y) (Y N Y) 2 N 1 standard deviation: the positive square root of the variance s Y = s Y 2 Exam Review: Measure of Dispersion four steps to calculate a variance: 1. Calculate the mean; 2. Compute the difference between each observation and the mean; and make sure that sum of Step #2 is 0; 3. Take the square of Step #2 and sum them up; 4. Divide the sum in Step #3 by N-1.

6 Exam Review: Measure of Dispersion five steps to calculate a standard deviation: 1. Calculate the mean; 2. Compute the difference between each observation and the mean; and make sure that sum of Step #2 is 0; 3. Take the square of Step #2 and sum them up; 4. Divide the sum in Step #3 by N-1; 5. Take the square root of Step #4. Exam Review: Measure of Dispersion What is the variance and standard deviation for the following data? Obs. # i Yi Yi-Y_bar (Yi-Y_bar)^ Y =? s 2 Y =? s Y = s 2 Y =? Exam Review Calculate the mean, median, mode, range, variance, and standard deviation for variable Y. Y 1 = 9, Y 2 = 6, Y 3 = 0, Y 4 = 1, Y 5 = 2, Y 6 = 9, Y 7 = 4, Y 8 = 6, Y 9 = 6, Y 10 = 9 Mode: Median: Mean: Range: Variance: Standard deviation:

7 Exam Review: Percentile and Z-Score two more tools for describing data percentile standardized score (Z-score) Make sure you are able to identify percentiles for continuous and ordinal variables using distribution table. compute Z-score for continuous variables. Exam Review: Percentile percentile: the value below which a given percentage of the observations in a distribution falls the Xth percentile: the lowest value at which the cumulative percentage equals or exceeds X% Exam Review: Percentile Value Frequency Percentage Cumulative Percentage 1 star 26% 26% 2 star 7% 33% 3 star 6% 39% 4 star 15% 54% 5 star 46% 100% the 25th percentile of this distribution? the 75th percentile? the median?

8 Exam Review: Percentile Construct a distribution table for the following variable 100 people were surveyed and asked how many phones they own. 12 people had zero phones, 58 people had one phone, 22 people had two phones, seven person had three phones, nobody had four phones, and one person had five phones. For the variable number of phones owned, generate a frequency distribution, a percentage distribution, and a cumulative percentage distribution. 20 percentile? 25 percentile? median? 90 percentile? Exam Review: Z-Score A standardized score or Z score describes the number of standard deviations an observation is above or below the mean. Y Y i Zi s Y example: Your vocabulary test score is 4. We know the mean score is 6.03 and a standard deviation What is your Z-score? Interpretation? Exam Review: Z-Score What is more unusual, a January that averages 25 degrees or a September that averages 65 degrees? January September Y 14.1 Y Jan Sep s 6.2 s 2. 7 Jan Sep

9 Exam Review: Graphs Why is the graph on the left misleading? Grade Point Average Men Women Grade Point Average Men Women Exam Review: Graphs What does the following graph tell us about income inequality in US? Exam Review: Probability and Normal Distribution basic ideas about inferential statistics probability normal distribution Make sure you are able to describe characteristics of the normal curve. identify proportions under the normal curves between Z-scores.

10 Exam Review: Probability probability: an expression of how likely it is that a particular outcome will result from a random event 0 probability 1 Exam Review: Normal Distribution characteristics of normal distribution curve 1. smooth, bell-shaped 2. symmetric with respect to the mean 3. Tails approach to the horizontal axis but never touch. Exam Review: Normal Distribution the location and height of a normal curve is determined by?

11 Exam Review: Normal Distribution μ 6 6 Exam Review: Normal Distribution The SAT Critical Reading scores in 2014 the US are normally distributed with mean μ Y=497 and standard deviation σ Y= % of the scores fall below? what percent of students have a score higher than 612?

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