Chapter 2 - Frequency Distributions

N

• the sample size of your full sample

n

• a sub-set of people/scores from within your full sample

Σ

• sum of a set of scores

Frequency Distribution

• organize data by the number of individuals located within each category of measurement

• a table or a graph

Frequency Distribution Table

• includes:

  • X (each possible score) — range from 0-5

  • F (frequency) — how many people got each score in the range

ΣX

• sum of the scores

Frequency Distribution Table — %

• % = F/N x 100

Grouped Frequency Distribution

• when there are a lot of possible scores

• group scores together to reduce the number of rows

Histogram

• a bar represents each score

• height of the bar = the frequency of that score

• the bars touch (because they’re on a continuous scale)

• graph for interval and ratio data

Distribution Polygon

• a dot represents each score

• height of the dot = the frequency of that score

• a line is drawn to connect the dots and then connects to the zero (because they’re continuous)

Bar Graph

• same as a histogram but the bars don’t touch

• the space reminds us that these are distinct, separate categories (not continuous, not related to each other)

Shapes of Frequency Distributions

• use curved lines when showing a population distribution

  • Symmetrical distributions (normal distribution…)

  • Skewed Distributions

Normal Distribution

• the curve is symmetrical with the highest frequency in the middle and lower frequencies in the extreme ends

Skewed Distributions

don’t follow the normal distribution that we would expect

• Positive Skew

  • tail is pointing to the higher (positive) numbers

• Negative Skew

  • tail is pointing to the lower (negative) numbers

Stem and Leaf Displays

• simple alternative to frequency tables and graphs

• tells you all the specific values

• the first digit(s) go on the left — stem

• the final digit goes on the right — leaf

Percentile Ranks

• to give a raw score more meaning in relation to other scores

  • e.g., I got 65 points on the test — but how did I compare to other?

• Percentile rank of a specific value = the % of people with scores equal to or less than that specific value

  • e.g,. if I scored in the 70th percentile, 70% of people scored lower than me

Calculating Percentile Ranks

• use a frequency table

  • cumulative frequency

  • cumulative percentage

Cumulative Frequency

• the number of people at or below that score

Cumulative Percentage

• the percentage of people at or below that score

Real Limits

• for continuous variables/scores

• each score has 2 “real limits” (.5 below and .5 above the actual score)

  • e.g., score = 150, lower real limit = 149.5; upper real limit = 150.5