# PSYC 241 Lecture Notes - Lecture 3: Normal Distribution, Level Of Measurement, Central Tendency

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Lesson 3: Central Tendency

● Central Tendency

○ Goal of Descriptive Statistics

■ To organize and summarize large groups of data

■ We want a handful of numbers that summarize a lot of numbers (we will also

use these measures for inferential stats as well)

○ Measures of Central Tendency

■ One number that summarizes all scores as an average

● Arithmetic Mean:

○ Sum data, divide by number of scores

○ Mean =

● Notation (symbols) for the mean

○ Population

■ µ =

○ Sample

■ ∑x/n

● Characteristics of the mean

○ Every time we add or subtract a score, we must recalculate the mean

○ If you +/- a score, the numerator and denominator both change

○ Transformation: smar mathematical operation to every score; just do the same to the

mean (used for inferential stats).

○ The mean is always our preferred measure of central tendency. Why?

■ Takes every score into account

■ Has a formula

■ Can easily transform scores

● Median

○ No formal symbol

■ Median = (n + 1)/2

○ Middle score

■ Exactly in the middle of distribution

■ Same number above and below

○ To calculate

■ Put scores in ascending order

■ Find score that's right in the middle

○ Very important for skewed distributions

● Mode

○ For categorical, nominal data

■ Most frequently occurring category or score

■ Can be determined for any scale of measurement

● Distributions

○ Normal distribution

■ These three numbers are the same

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