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# BU PSYC 243 - Frequency Distribution & Central Tendency

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PSYC 243 1st Edition Lecture 4Outline of Last Lecture I. Classification of Variablesa. Broad Classification of Variablesb. 4 Types of Measurement Scales (more classification)c. Why does any of this matter? II. Frequencya. Describing a single variableb. Rfc. Frequency Distributiond. Displaying Frequency information in a graphOutline of Current Lecture I. Frequency Distributionsa. Normal Distributionb. Positively skewedc. Negatively Skewedd. Bimodal Distributione. Important Notef. 2 Very Important General PointsII. Central Tendencya. What is the most representative score?b. The Medianc. The Meand. The Modee. Why Mode isn’t greatf. Which Measure of Central Tendency should you use?Current LectureFrequency Distributions- Useful to compare shapes- Any shape is possible- Some shapes occur frequentlyo Normal distributiono Bimodalo Skewed positive & negativeThese 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.Normal Distribution- 1 peak unimodal distribution- Symmetrical distribution extremely low & extremely high scores are equally (in)frequent- Most frequent type of distribution- Most human characteristics are normally distributed height, IQ etc. - Most statistical formulas are based on assumption of normalcy of dataPositively Skewed- A few extremely high scores are raising the tail on the right not balanced with corresponding low scores- Company salaries, Reaction times, age of students in class, marathon timesNegatively Skewed- A few extremely low scores are raising the tail on the left. It is not balanced with corresponding high scores- Exam gradesBimodal Distribution- 2 high frequency peaksNote:- Idealized distribution: the data you collect probably won’t look this good- Statistical formulas were developed based on normal distribution, but many statistical formulas are still valid even if you have non-normal data- Techniques to make data resemble a normal distributiono Eliminate outlierso Transform the data- Extraneous factors can affect distribution2 Very Important General Points- Samples resemble their populations o Frequency distributions of samples generally have approximately the same shapeas the population it was drawn fromo Mean of sample should be similar to the mean of populationo Exception: Samples have more “spread” than samples- Different samples drawn from the same population should resemble each other o Similar looking frequency distributiono Similar meansCentral TendencyWhat is the Most Representative Score? Is There a Single Number to Summarize?- Could be:o Most frequent scoreo Mathematical average of all scoreso Middle position on frequency distribution shapeThe Median- The score at 50th percentile exactly half the scores are lower than the median & exactly half the scores are high - How to find: Line up all the scores from high to low- find the score at the middle portion if N is odd; average the 2 middle scores if N is even- Impractical for large samplesThe Mean- The mathematical center of distribution- How to find: add all of the scores together then divide by NThe Mode- Score that occurs most frequently in a sample- How to find: construct a frequency chartWhy Mode Isn’t Great- Ignores all data except the most frequently occurring score (or scores if bimodal)Which Measure of Central Tendency Should You Use?- Use the mean UNLESS:o You have nominal data, use the mode to find the averageo If you have a skewed distribution, use the median or the mode. Using the mean can be misleading can give an inflated pictureo You have ordinal date use the median**If your data are normally distributed & you have a large enough N, the mean, mode & median will be equivalent. In real life, with smaller samples they will be closer, but not

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