PSY201: Chapter 2 - Frequency Distributions

Question 1

Frequency Distributions basics

Answer 1

simplifying + organizing data

organized tabulation showing exactly how many individuals located in each category on scale of measurement

Question 2

Frequency Distributions basics

Answer 2

presents an organized pic of entire set of scores

shows where each individual is located relative to others in distribution

Question 3

Frequency Distributions Tables

Answer 3

2 columns - 1 listing categories (X) + 1 for frequency (f)

X column, values listed from highest to lowest, without skipping any

Question 4

Frequency Distributions Tables

Answer 4

frequency column - tallies determined for frequencies for each X value
sum of frequencies should equal N

Question 5

Frequency Distributions Tables

Answer 5

3rd column - proportion (p) for each category: p = f/N
sum of the p column = 1.00
4th column - % of distribution corresponding to each X - multiplying p by 100
sum of the % column = 100%.
5th column for cumulative percent

Question 6

Regular Frequency Distribution

Answer 6

Summarizes sets of data that require little additional organization
data span relatively narrow range of values/categories
All raw data shown

Question 7

Grouped Frequency Distribution

Answer 7

Used when set of scores covers wide range of values

Group data into intervals – ranges of values - to make easier to understand

Question 8

Grouped Frequency Distribution

Answer 8

X column lists groups of scores - class intervals

Question 9

Grouped Frequency Distribution Rules

Answer 9

1. interval width selected so table has approx 10 class intervals
2. Width simple number (2, 5, 10)

Question 10

Grouped Frequency Distribution Rules

Answer 10

3. Bottom score in each class interval multiple of width
width of 10, bottom score multiple of 10
4. Intervals should all have the same width & cover complete range scores

Question 11

Grouped Frequency Distribution

Answer 11

Real Limits
Advantage of no ambiguity of class membership
No gaps
easily transformed into graphical representation (frequency histogram), directly from table

Question 12

Frequency distribution graphs

Answer 12

Visual representation of frequencies
Useful because they show the entire set of scores
can determine highest score, lowest score, + where scores are centered
shows whether scores clustered together/scattered over wide range

Question 13

Frequency distribution graphs

Answer 13

In most, X values listed on the X axis + frequencies listed on the Y axis

Question 14

Frequency distribution graphs

Answer 14

X consist of numerical scores from interval/ratio scale ⇒ histogram/polygon
nominal/ordinal ⇒ bar graphs

Question 15

Graphs for Interval/Ratio scales: Histograms

Answer 15

Bar centered above each score/class interval  
height of bar = frequency + width extends to real limits
adjacent bars touch

Question 16

Graphs for Interval/Ratio scales Polygons

Answer 16

dot centered above each score - height of dot = frequency
join dots with straight lines
additional line drawn at each end to bring graph back to zero frequency

Question 17

Polygons

Answer 17

for plotting frequency of continuous variables
Communicates same info
shape of distribution emphasized
Can be superimposed on a histogram

Question 18

Graphs for Nominal or Ordinal data: Bar graphs

Answer 18

X nominal/ordinal
gaps/spaces left betw adjacent bars
scale made up of distinct categories – not continuous/not necessarily same size

Question 19

Pie charts

Answer 19

-

Question 20

Relative frequency

Answer 20

Many pops so large - impossible to know exact frequency

distributions can be shown using relative frequency instead

Question 21

Smooth curve

Answer 21

scores in pop measured on interval/ratio scale ⇒ present distribution as smooth curve not a jagged polygon
emphasizes fact that distribution not showing exact frequency for each category

Question 22

Shape

Answer 22

graph shows shape of distribution

symmetrical if left side of the graph is (roughly) mirror image of the right side

Question 23

Shape

Answer 23

bell- shaped normal distribution

skewed - scores pile up on one side of the distribution, leaving “tail” of few extreme values on other side

Question 24

positively skewed distribution

Answer 24

scores tend to pile up on left side of the distribution with tail tapering off to the right

Question 25

negatively skewed distribution

Answer 25

scores tend to pile up on the right side + tail points to the left

Question 26

Grouped Frequency Distribution

Answer 26

values in intervals ⇒ apparent limits of the interval

upper + lower boundaries involve real limits

Question 27

Stem-and-Leaf Displays

Answer 27

stem-and-leaf display provides very efficient method for obtaining + displaying frequency distribution
Each score divided into stem consisting of first digit/digits, + leaf consisting of final digit

Question 28

Stem-and-Leaf Displays

Answer 28

write leaf for each score beside its stem
organized picture of entire distribution
number of leafs beside each stem = frequency
individual leafs identify individual scores.

Question 29

Percentile Ranks

Answer 29

relative location of individual scores within a distribution

percentage of individuals with scores equal to/less than X value

Question 30

Interpolation

Answer 30

cumulative % identifies percentile rank for upper real limit

Question 31

Interpolation

Answer 31

mathematical process based on assumption that scores + % change in regular, linear fashion as you move through interval from one end to other

Question 32

Interpolation

Answer 32

1. Find width of interval on both scales.
2. Locate position of intermediate value in interval
   fraction = distance from top of interval/interval width
3. Use fraction to determine distance from top of interval on other scale
   distance = fraction x width (of scale we want to find)
4. Use distance from top to determine position on other scale

Question 33

linear interpolation

Answer 33

“Assumption of linearity permits computation of intermediate percentile ranks and percentiles

Question 34

Interpolation

Answer 34

single interval measured on 2 separate scales endpoints known
Given intermediate value on 1 of the scale task is to estimate corresponding intermediate value on other scale.