# PSYCH 100A Lecture Notes - Lecture 3: Central Tendency, Standard Deviation

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Published on 28 Mar 2018

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Distributions

• Can be a graph/table/mathematical function describing the frequency of each score

• Frequency describes how often something occurs

• The normal distribution is a theoretical function that describes many physical and

psychological traits

o Apex of the curve is the highest occurrence at the middle

▪ Center of distribution is important

• Typical score

o Lower tail/upper tail is where the curve levels off

▪ Region where uncommon scores occur

o Bell-curve

Theoretical vs. Empirical Distributions

• Center: represents typical response, lower spread (high peak)

• Spread - (or variability) like standard deviation, sample of scores where people are more

similar to one another. Low peak

o High variability - low peak

o Low variability - high peak, scrunched up

• Shape - depends on where the peak is

o In what area do most scores fall?

• Positively skewed distribution

o Most scores in the low range, high scores are less frequent

o Tail point towards the positive side of the number line

• Negatively skewed distribution

o Most scores in the high range, low scores are less frequent

o Tail points toward the negative side of the number line

• Uniform distribution

o All scores equally likely

Distributions

• How can we summarize the distribution

Bar Graphs and Histograms

• Bar graphs: categorical variable

o Put spaces between the bars to categorize it, not continuous number line but bins

o Order of the bars are arbitrary. Can't say that it is positively/negatively skewed.

• Histograms: continuous variable

o No spaces between the bars

o Kernel Density Plot - connects the heights of all the bars in a histogram

▪ Represents a continuous function

Frequency Distributions

• A tabular display of the information from the bar graph

Cumulative Percent

• The percentage at or below a score

• Accumulate the two percentages from the bottom two categories

o "15% of the people participating in the study were at or below inappropriate"

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