Chapter 5 Descriptive Statistics (Psy 300 Lect)

Front 1

Frequency Distribution

Back 1

A table in which all of the scores are listed along with the frequency with which each occurs.

Front 2

Qualitative Variable

Back 2

a categorical variable for which each value represents a discrete category.

Front 3

Quantitative Variable

Back 3

a variable for which the scores represent a change in quantity.

Front 4

Do a frequency table for 5,4,4,3,3,3,2,2,2,1

Back 4

Try it now GO !

Front 5

Class Interval Frequency Distribution

Back 5

When the number of categories is very large, they are combined, or grouped, in the table.

Front 6

How do you do an Interval Frequency Distribution ?

Back 6

Individuals scores are combined into categories, or intervals and then listed along the frequency of scores in each interval.

Front 7

Graphs

Back 7

1. Bar graphs

2. Histograms

3. Frequency of polygons.

Front 8

Creating a Histogram

Back 8

1. List all the numeric scores on the X axis.

2. Y Axis should be the frequency of scores.

Front 9

Bar Graph

Back 9

Front 10

Frequency Distribution Histogram

Back 10

Front 11

Histogram

Back 11

Front 12

Frequency Distribution Histogram for Grouped Data

Back 12

Front 13

Frequency Polygon

Back 13

Front 14

Descriptive Statistics

Back 14

Numerical measures that describe a distribution by providing:

1. Information on the central tendency of the distribution.

2. The width of the distribution

3. The shape of the distribution,

Front 15

What are the characteristics of descriptive statistics?

Back 15

1. Information on the central tendency of the distribution,

2. The width of the distribution,

3. The shape of the distribution,

Front 16

Measure of central tendency

Back 16

a number that characterizes the "middleness" of an entire distribution.

Front 17

Types of measures of central tendency

Back 17

1. Mean

2. Median

3. Mode

Front 18

Mean

Back 18

The average

Sum of scores / the amount of scores.

Used with interval and ration data

Front 19

Median

Back 19

The middle score in a distribution of scores organized from highest to lowest or vice-versa.

Used with Ordinal, Interval, and ratio data.

Front 20

Mode

Back 20

The score occurring with the greatest frequency.

Nominal, ordinal, interval, or ratio data.

Not a reliable measure of central tendency.

Front 21

µ

Back 21

Population mean = ∑x / N

Front 22

x̅

Back 22

Sample mean = ∑x / N

Front 23

What is the median of 3, 5, 8, 10, 11

Back 23

Median = 8

Front 24

Distribution of even numbers,

3, 3, 4, 5, 7, 8

Back 24

4+5/2 = 9/2 = 4.5

Front 25

Bimodal Distribution

Back 25

Major and Minor Modes.

Front 26

Find mean, median, and mode for the following data:

5, 15, 10, 15, 5, 10, 10, 20, 25, 15

Back 26

Mean : 13

Median: 12.5

Mode: Major = 15 Minor =10

Front 27

Variability

Back 27

A quantitative measure of the differences between scores.

Front 28

Purposes of Measure of Variability

Back 28

1. Describes the distribution

2. Measure how well an individual score represents the distribution.

Front 29

What are three measures of variability

Back 29

1. The Range

2. The standard deviation

3. The Variance

Front 30

The range

Back 30

The distance covered by the scores in a distribution.

Measured from smallest value to highest value.

Front 31

Formula for Range

Back 31

range = URL for Xmax — LRL for Xmin

Front 32

Standard Deviation and Variance for a population

Back 32

Most common and most important measure of variability.

Describes whether the scores are clustered closely around the mean or widely scattered.

Front 33

Deviation

Back 33

is the distance from the mean

Deviationscore = X — μ

Front 34

What is the deviation score if

µ = 50 and x = 45

Back 34

Deviationscore = X — μ

Deviationscore = 45 — 50

Deviationscore = X — 5

Front 35

Mean of Deviations

Back 35

X -- µ = should equal 0

Then take the mean of those scores.

Front 36

Variance is

Back 36

the average squared distance from the mean.

Average of the squared deviations

Front 37

Formula for variance

Back 37

σ² = Σ (X –μ) ² / N

Front 38

Standard Deviation

Back 38

= Square root of Variance

Front 39

μ =

Back 39

population mean

Front 40

σ =

Back 40

standard deviation

Front 41

σ2 =

Back 41

variance

Front 42

SS =

Back 42

sum of squares

Front 43

Practice the Formula on Slide 45

Back 43

Do IT !!!

Front 44

Normal Curve

Back 44

a symmetrical, bell-shaped frequency polygon representing a normal distribution,

Front 45

Normal distribution

Back 45

a theoretical frequency distribution that has certain special characteristics.

Front 46

Kurtosis

Back 46

how flat of peaked a normal distribution is

Front 47

Mesokuritc

Back 47

Normal curves that have peaks of medium height and distributions that are moderate in breadth.

Front 48

Leptokurtic

Back 48

Normal curves that are tall and thin, with only a few scores in the middle of the distribution having a high frequency.

Front 49

Platykurtic

Back 49

Normal curves that are short and more dispersed.

Front 50

Postive Skew

Back 50

Tail on the right.

Front 51

Negative Skew

Back 51

Tail on the left.

Front 52

Purpose of Z-Scores

Back 52

Identify and describe the location of every score in the distribution.

Standardizes an entire distribution

Front 53

The location is described by z-score

Back 53

Sign + or - tells whether the score is located above or below the mean.

Number tells the distance between score and mean in standard deviation units.

Front 54

Z-score = +1

Back 54

1 Standard deviation above the mean.

Front 55

Z-score (Standard Score)

Back 55

a number that indicates how many standard deviation units a raw score is from the mean of a distribution.

Front 56

Z score for Sample

Back 56

Front 57

z score for Population

Back 57

Front 58

Practice calculting

Back 58

raw score from z score.

Front 59

Practice calculating

Back 59

µ from z score.

Front 60

Probability

Back 60

the expected relative frequency of a particular outcome.

Front 61

Area between Mean and Z

Back 61

area under the curve between the mean of the distribution, and the z score with which you are working.

Front 62

Area beyond Z

Back 62

area under the curve from the z-score out to the tail end of the distribution.