Descriptive Statistics

Question 1

Frequency Distributions (three types)

Answer 1

1. Simple (ungrouped) frequency distribution
2. Grouped frequency distribution
3. Cumulative Frequency distribution

Question 2

Simple (ungrouped) frequency distribution

Answer 2

Response option in the left column (ethnicity), frequency in the middle, and percent in right hand columns

Question 3

Grouped frequency distribution

Answer 3

Left hand column has responses grouped so data can be summarized

Question 4

Cumulative frequency distribution

Answer 4

Cumulative percent included

Question 5

Stem and Leaf Display

Answer 5

• Like a grouped frequency distribution without loss of information
• Stem: The intervals on the left
• Leaf: Digits on the right side indicating frequency and number

Question 6

Histograms

Answer 6

• Vertical columns indicating frequency
• Baseline (or horizontal) axis corresponds with observed scores
• Vertical axis labeled with frequencies
• Bar graph is the same as a histogram except it presents qualitative data (e.g., gender, ethnicity, etc.)

Question 7

Normal Distribution

Answer 7

Most of the scores are clustered near the middle of the continuum of observed scores
-Resembles bell shape curve

Question 8

Skewed Distribution

Answer 8

Most of the scores are clustered on one end of the continuum

• Positively skewed: Scores cluster at the lower end of the continuum (higher than zero statistic)
• Negatively skewed: Scores cluster at the higher end of the continuum (lower than zero statistic)

Question 9

Kurtosis

Answer 9

Measure of the degree of peakedness of a distribution

• Leptokurtosis: Distribution is too peaked with thin tail (higher than zero statistic)
• Platykurtosis: Distribution is too flat with many cases in the tail(s) (lower than zero statistic)

Question 10

Multimodal Shapes

Answer 10

Scores tend to congregate around more than one point

• Bimodal: Scores are clustered in two places
• Trimodal: Scores are clustered in three places

Question 11

Mode

Answer 11

Most frequently occuring score

Question 12

Median

Answer 12

Midpoint

Question 13

Mean

Answer 13

Average

Question 14

Degree of dispersion of scores

Answer 14

Similarity and dissimilarity between scores

Question 15

Homogenous scores

Answer 15

Similar and have no variability

Question 16

Heterogeneous scores

Answer 16

Dissimilar and have high variability

Question 17

Range

Answer 17

Difference between the highest and lowest scores

Question 18

Interquartile range

Answer 18

Spread between the middle 50% of the scores

• Upper Quartile: Top 25%
• Lower Quartile: Bottom 25%

Question 19

Box-and-whisker plot

Answer 19

Summarizes the degree of variability with a picture

• “Box” indicates the middle 50% of scores
• “Whiskers” extend to highest score, 1.5 times the height of the rectangle, or to the 5th and 95th percentile
• Line in the middle corresponds with median
• Helps identify outliers

Question 20

Outliers

Answer 20

• Scores that lie far away from the data set
• Why do they occur?
• -Sabotage
• -Misunderstandings
• -Extreme thinking

Question 21

What should you do with outliers?

Answer 21

• Conduct analyses with and without

- Some outliers are of interest (e.g., they can call attention to a poorly worded question)

Question 22

Standard Deviation (SD)

Answer 22

• Figuring out how much each score deviates from the mean

* Putting deviation into formula

Question 23

Variance (S^2)

Answer 23

Standard deviation squared

Question 24

Standard Scores

Answer 24

• Describe relative position

* Derived from the manipulation of a raw score that indicates distance from the mean

Question 25

T & Z-scores

Answer 25

Both indicate how many standard deviations a raw score is above or below the group mean

Question 26

Z-scores

Answer 26

Scores begin at 0 and thus a score of 2.0 would indicate two standard deviations about the mean

Question 27

T-Scores

Answer 27

Take z-score, multiply it by 10, and then add 50