2: Descriptive Stats For Distirbutions Part 1

Question 1

Data matrices

Answer 1

Data organized into a grid format

• row= case
• column=variable
• cell=value

Question 2

Frequency tables

Answer 2

Showing the number of cases with each value of a variable

• calculate %
• works best for categorical or discrete variables
• for Quan that take many values report binned within certain ranges
• hard to extract more detailed information or easily grasp shape of distribution

Question 3

Categorical variables (nominal data)

Answer 3

Pie graphs visually represent proportions or %

Question 4

Stemplots

Answer 4

Graphical with all values of a quantitative variable

Question 5

Frequency histograms

Answer 5

Display the frequency distribution of one variable
-possible values of variable on X
-frequency of each variable on Y
Height = frequency
-for continuous variables: values binned into ranges
-as number of measurements increases, a frequency histogram approximats a curved shape

Question 6

Normal distribution

Answer 6

Specific shape of frequency:
-bell shaped
-symmetrical
-

Question 7

Positive skew

Answer 7

Tail to the right. (Most values on left)

• floor effects: cluster at low end
• high outliers

Question 8

Negative skew

Answer 8

Tail to left (most values on right)

• ceiling effects (many cluster at high end)
• low outliers

Question 9

Central tendency

Answer 9

• center of distributions

- mode,median,mean

Question 10

Describing variability

Answer 10

Spread of distribution

-range, standard deviation

Question 11

Mode

Answer 11

Most frequently occurring

• near center if normal
• may have multiple modes (bimodal) non normal
• values other than most frequent not considered
• limited application for continuous variables

Preferred when:

• discrete data
• nominal scale
• multimodal

Question 12

Median

Answer 12

Value at midpoint

• resistant to outliers
• takes more info into account than mode, but still ignores magnitudes

Preferred when;

• skewed distribution
• ordinal scale

Question 13

Mean

Answer 13

Average of all values

• sensitive to outliers
• most informative

Preferable when:

• interval or ratio
• normal distribution

Question 14

Skewed distribution

Answer 14

Median remains stable near center,

-outliers pull the mean in the direction of tail

Question 15

Multimodal

Answer 15

Modes may be most informative

-mean and median may not represent the typical value

Question 16

Range

Answer 16

Max-min

• very sensitive to outliers
• values between extremes not accounted for

Preferred if Max and min relevant

Question 17

Interquartile range

Answer 17

Defines the range of middle 50% 
-Q1: median lower half
-Q3: median of upper half
These are boudriesnif middle 50%
-very resistant to outliers 
-more info than range but still ignores the magnitude of most values. 
IQR= Q3-Q1

Simple rough estimate

Question 18

Standard deviation

Answer 18

Variance: S^2 average squared deviation of each score from mean

Standard deviation is square root of variance
Variance= sum(X-M)^2/N-1

-most widely used
-sensitive to outliers
-take all scores
Preferred in most cases if normal distribution

Question 19

Five number summary

Answer 19

Max score
Third quartile
Median
First quartile
Min score

• resistant measure of center
• resistant measure of spread
• sensitive measure of outer limits of spread

Question 20

Box plots

Answer 20

Values of variable Y
First and third quartile ends in box
A line in box is median
Whiskers max and min scores