Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Part II Sigma Freud & Descriptive Statistics Chapter 2 Means to an End: Computing and Understanding Averages What you will learn in Chapter 2 Measures of central tendency Computing the mean and weighted mean for a set of scores Computing the mode using the mode and the median for a set of Selecting a measure of central tendency Measures of Central Tendency The AVERAGE is a single score that best represents a set of scores Averages are also know as “Measure of Central Tendency” Three different ways to describe the distribution of a set of scores… Mean – typical average score Median – middle score Mode – most common score Computing the Mean SX X n Formula for computing the mean “X bar” is the mean value of the group of scores “S” (sigma) tells you to add together whatever follows it X is each individual score in the group The n is the sample size Things to remember… N = population n = sample Sample mean is the measure of central tendency that best represents the population mean Mean is VERY sensitive to extreme scores that can “skew” or distort findings Average means the one measure that best represents a set of scores Different types of averages Type of average used depends on the question Weighted Mean Example List all values for which the mean is being calculated (list them only once) List the frequency (number of times) that value appears Multiply the value by the frequency Sum all Value x Frequency Divide by the total Frequency (total n size) Weighted Mean Flying Proficiency Test(Salkind p. 23) Value Frequency Value*Freq 97 94 92 91 4 11 12 21 388 1,034 1,104 1,911 90 89 78 30 12 9 2,700 1,068 702 60 Total 1 100 60 8967 You Try!! Using Weighted Mean to Find Average Super Bowl Yardage Penalty Value Frequency 5 (ie. False starts, illegal downfield) 4 10 (offensive holding) 4 11 (Half the distance penalties on kickoffs/punts) 3 15 (personal fouls) 2 Value*Frequency Computing the Median Median = point/score at which 50% of remaining scores fall above and 50% fall below. NO standard formula Rank order scores from highest to lowest or lowest to highest Find the “middle” score BUT… What if there are two middle scores? What if the two middle scores are the same? A little about Percentiles… Percentile points are used to define the percent of cases equal to and below a certain point on a distribution 75th %tile – means that the score received is at or above 75 % of all other scores in the distribution “Norm referenced” measure allows you to make comparisons Cumm Percentage of Ages (N=20) Ages freq % Cumm % 15-19 6 .30 .30 20-25 4 .20 .50 26-30 5 .25 .75 31-35 5 .25 1.00 Computing the Mode Mode = most frequently occurring score NO formula List all values in the distribution Tally the number of times each value occurs The value occurring the most is the mode Democrats = 90 Republicans = 70 Independents = 140 – the MODE!! When two values occur the same number of times -- Bimodal distribution Using Calculator Mode + . = statistical mode; Shift +7= the mean “x-bar” Shift +5= sum of x; square this value to get square of the sum; Shift +4 = sum of squares Shift +9= sample standard deviation Shift+1=permutations Shift+2=combinations When to Use What… Use the Mode Use the Median when the data are categorical when you have extreme scores Use the Mean when you have data that do not include extreme scores and are not categorical Measures of Central Tendency Choosing the right measure Normal distribution Mean: = median/mode Median: = mean/mode Mode: = mean/median They all work. Pick the one that fits the need. Chapter 3 15 Measures of Central Tendency Choosing the right measure Positively skewed Mean: little high Median: middle score Mode: little low Median works best Chapter 3 16 Measures of Central Tendency Choosing the right measure Negatively skewed Mean: too low Median: middle score Mode: little high Median works best Chapter 3 17 Central Tendencies and Distribution Shape Using SPSS Glossary Terms to Know Average Measures of Central Tendency Mean Median Weighted mean Arithmetic mean Percentile points outliers Mode