1. 10.5 Organizing & Displaying Date
Math Models
Unit 10 Statistical Data Analysis

2. Skewed (left or right)
refers to data that is spread far and thinly toward one side
the direction of skewness is on the side of the longer tail

3. Descriptive Terms of Population Models
Two Examples of Skewed Right

4. Used to plot frequency of discrete data.
Dot Plots -Dot plots are used to illustrate a small amount of data in order to see the shape of distribution,
Used to plot frequency of discrete data.
Dots must be lined up horizontally
Vertical axis is frequency of occurrence
Advantages
integrity of data maintained
Easy to see distribution of data

5. Example: Jennifer counted the amount of matches in 20 boxes and noted the results below:
47, 49, 45, 50, 52
51, 50, 49, 49, 50
50, 48, 51, 50, 51
50, 49, 50, 47, 52
Illustrate this data on a dot plot.

7. Dotplots Item Amount Tuition fees $5,000 Room and board 9,000
Books and lab
2,000
Clothes/cleaning
1,000
Transportation
Insurance and miscellaneous

8. Stem and Leaf Plots
Definition: A plot where each data value is split into a "leaf" (usually the last digit) and a "stem" (the other digits). For example "32" is split into "3" (stem) and "2" (leaf). The "stem" values are listed down, and the "leaf" values are listed next to them.

9. Stem and Leaf Plots Legend 8 | 1 = test score of 81
Test Scores out of 105
Stem is a place holder
- in this case , 10’s
Leaf is the last digit
Stem
Leaf 5 6
3 5 7 8 9 10
Legend 8 | 1 = test score of 81

10. Comparative Stem and Leaf Plot
Price of Homes in Ten Thousands
West El Paso
Central El Paso 15
2 2 16
2 3 5 17 5 18
1 4 4
9 2 19 2 20 21 22 23
Legend 18 | 1 = home price of $181,000

11. Stem and Leaf Plots Integrity of data maintained
Easy to visualize distribution of data
Comparative plots work well

12. Box Plots Data is organized from smallest to largest.
Scale is based on data
Width of each segment of box indicates density of data
Wide segment means data frequency is not as dense
25% of the data is in each quartile
Quartiles can be found by using 1VARSTAT on calculator

13. How to construct find five-number summary Min Q1 Med Q3 Max
draw box from Q1 to Q3
draw median in the box
extend whiskers to min & max

14. Modified Box Plots Outlier Q3 Median Q1 670 590 530 Max Min 740 280
Verbal SAT scores
280, 340, 440, 490, 520, 540, 560, 560, 580, 580,
600, 610, 630, 650, 660, 680, 710, 730, 740, 740
Outlier Q1
530
Median
590 Q3
670
Min
280
Max
740

15. Calculating Outliers
IQR = Q3 – Q1 (IQR is a number, not a range of numbers)
IQR is the range of the middle 50% of the data
Outliers occur outside of “fences”
Data smaller than Q1 – 1.5*(IQR)
Data larger than Q *(IQR)
Each outlier is indicated with a dot, or asterix

16. Interquartile Range (IQR) – is the range (length) of the box
Outlier Fence
Q1 – 1.5(IQR)
Q (IQR)
Interquartile Range (IQR) – is the range (length) of the box
Q3 - Q1
Any observation outside this fence is an outlier! Put a dot for the outliers.

17. Boxplots Organizes data into segments which is easy to quickly analyze
Useful for comparative displays
Convenient display of outliers
Great for large data sets
Should not be used for data sets smaller than 10
Raw data is lost
Can only estimate mean

18. Histograms They are NOT bar graphs
Used for discrete AND continuous data
A frequency chart must be created
Intervals defined
Example of interval for continuous 0 ≤ x < 10, 10 ≤ x < 20
Example of interval for discrete 0 ≤ x ≤ 9, 10 ≤ x ≤ 19
Count of data that falls into each interval is recorded
The vertical axis is Frequency
Horizontal axis is based off of intervals

19. Example Frequency Chart
Interval
Freq
0 ≤ x < 5 8
5 ≤ x < 10 6
10 ≤ x < 15 4
15 ≤ x < 20 2
20 ≤ x < 25
25 ≤ x < 30
30 ≤ x < 35

20. Histograms Class Interval Frequency 1 $1-$5 8 2 $6-$10 6 3 $11-$15 4
$16-$20 5
$21-$25
$26-$30 7
$31-$35

21. Histograms Easy to visualize distribution of data Raw Data is lost
Can estimate mean, median, standard deviation
Use calculator – input in list one the median value of each bar
In list two, input each frequency (height of bar)
1VARSTAT using L2 as FREQ LIST