1. Ch. 10: Summarizing the Data

2. Criteria for Good Visual Displays
Clarity
Data is represented in a way closely integrated with their numerical meaning.
Precision
Data is not exaggerated.
Efficiency
Data is presented in a reasonably compact space.

3. Frequency Distribution Example

4. Bar Graphs Example

5. Stem-and-Leaf Chart
Stems
Leaves 8 2 7 4 9 6 5 1 3

6. Back-to-Back Stem-and-Leaf Chart
Depression
Stems
Hypomania 2 5 8 1 6 4 3

7. Measures of Central Tendency: Determining The Median
Arrange scores in order
Determine the position of the midmost score: (N+1)*.50
Count up (or down) the number of scores to reach the midmost position
The median is the score in this (N+1)*.50 position

8. Measures of Central Tendency: The Arithmetic Mean
The balancing point in the distribution
Sum of the scores divided by the number of scores, or

9. Measures of Central Tendency: The Mode
The most frequently occurring score
Problem: May not be one unique mode

10. Symmetry and Asymmetry
Symmetrical (b)
Asymmetrical or Skewed
Positively Skewed (a)
Negatively Skewed (c)

11. Comparing the Measures of Central Tendency
If symmetrical: M = Mdn = Mo
If negatively skewed: M < Mdn  Mo
If positively skewed: M > Mdn  Mo

12. Measures of Spread: Types of Ranges
Crude Range: High score minus Low score
Extended Range: (High score plus ½ unit) minus (Low score plus ½ unit)
Interquartile Range: Range of midmost 50% of scores

13. Measures of Spread: Variance and Standard Deviation
Variance: Mean of the squared deviations of the scores from its mean
Standard Deviation: Square root of the variance

14. Summary Data for Computing the Variance and Standard Deviation
Raw scores
X - M
(X – M)2 2 -3 9 4 -1 1 5 7 8 3
X = 30
(X – M) = 0
(X – M)2 = 24
M = 5

15. Descriptive vs. Inferential Formulas
Use descriptive formula when:
One is describing a complete population of scores or events
Symbolized with Greek letters
Use inferential formula when:
Want to generalize from a sample of known scores to a population of unknown scores
Symbolized with Roman letters

16. Variance: Descriptive vs. Inferential Formulas
Descriptive Formula
Inferential Formula
Called the “unbiased estimator of the population value”

17. Confidence Interval for a Mean

18. Values of x (for df =5) for Five Different Confidence IntervalsCI x
t(x) (for df = 5)
99.9%
.001
6.87
99%
.01
4.03
95%
.05
2.57
90%
.10
2.02
80%
.20
1.48

19. The Normal Distribution
Standard Normal Distribution: Mean is set equal to 0, Standard deviation is set equal to 1

20. Standard Scores or z-scores
Raw score is transformed to a standard score corresponding to a location on the abscissa (x-axis) of a standard normal curve
Allows for comparison of scores from different data sets.

21. Raw Scores (X) and Standard Scores (z) on Two Exams
Student ID and gender
Exam 1
Exam 2
Average of z1 and z2 scores
X1 score
z1 score
X2 score
z2 score
1 (M) 42
+1.78 90
+1.21
+1.50
2 (M) 9
-1.04 40
-1.65
-1.34
3 (F) 28
+0.58 92
+1.33
+0.96
4 (M) 11
-0.87 50
-1.08
-0.98
5 (M) 8
-1.13 49
6 (F) 15
-0.53 63
-0.33
-0.43
7 (M) 14
-0.62 68
-0.05
-0.34
8 (F) 25
+0.33 75
+0.35
+0.34
9 (F)
+1.61 89
+1.16
+1.38
10 (F) 20
-0.10 72
+0.18
+0.04
Sum ()
212
688
Mean (M)
21.2
68.8
SD ()
11.69
1.0
17.47
0.98