1. 1.2 Dotplots, Stem & Leaf, Histograms
I can…
-Make a dotplot or stemplot to display small sets of data.
-Describe the overall pattern (shape, center, spread) and identify outliers.
-Identify the shape of a distribution from a dotplot, stemplot or histogram as roughly symmetric or skewed. Identify the number of modes.
-Make a histogram with a reasonable choice of classes.
-Interpret histograms.

2. Dotplot Make dotplot on board
# of siblings 2,0,3,2,0,0,1,5,2,1,3,1,2,1,2,1,1,1,2,1,1,2,1,2,3,6,1,2

3. Siblings Dotplot…Outliers
Identify any potential outliers.

4. Siblings Dotplot…Shape
Describe the shape
Roughly symmetric,
skewed right, or
skewed left?
Unimodal,
Bimodal, or
Multimodal?

5. Vocabulary
A symmetric distribution has values to the left and the right of the midpoint that are mirror images of one another
Skewed
Left skewed – the left tail (values to the left of the midpoint) is much longer than the right tail (values to the right of the midpoint)
Right skewed - the left tail is much longer than the right tail

6. Vocabulary Modes – the major peaks in a distribution
Unimodal – a distribution with one major peak
Bimodal – a distribution with two major peaks
Multimodal – a distribution with multiple major peaks

7. Siblings Dotplot…Center
Describe the center of the distribution.
Mean
Mode
Median

8. Siblings Dotplot…Spread
Describe the spread or variability of the distribution.
Range

9. Siblings Dotplot for our class
Compare our dotplot to the one provided.

10. AP Exam Common Error
When asked to compare distributions, often students discuss each distribution separately…No credit!
You must use phrases like “about the same as” or “is much greater than”.
Don’t forget to think/write…compared to what…

11. Stem and Leaf Plots Make stem and leaf on board
How many pairs of shoes does a typical male
teenager have?
14, 7, 6, 5, 12,
38, 8, 7, 10, 10,
10, 11, 4, 5, 22,
7, 5, 10, 35, 7
Make stem and leaf on board
How many pairs of shoes does a typical female teenager have?
50, 26, 26, 31, 57, 19, 24, 22, 23, 38, 13, 50, 13, 34, 23, 30, 49, 13, 15, 51

12. Splitting Stems
4 9

13. Comparing Stem & Leaf Plots
Compare the # of pairs of shoes owned by males and females. Be sure to address shape, outliers, center, and spread.

14. Stemplot Tips
Stemplots do not work well for large data sets, where each stem must hold a large number of leaves.
There is no magic number of stems to use, but five is a good minimum.
If you split stems, be sure that each stem is assigned an equal number of possible leaf digits
You can get more flexibility by rounding the data so that the final digit after rounding is suitable as a leaf. Do this when the data have too many digits.
Salary Example $42, 849…$43,000

15. Using Stem Plots to Analyze Data
The chart on the next slide plots the literacy rates between men and women in Islamic countries
We are going to analyze the plot to draw conclusions about our data.

16. Literacy Rates in Islamic Countries
Country
Female %
Male %
Algeria 60 30
Bangladesh 31 50
Egypt 46 68
Iran 71 85
Jordan 86 96
Kazakhstan 99
100
Lebanon 82 95
Libya 92
Country
Female %
Male %
Malaysia 85 92
Morocco 38 68
Saudi Arabia 70 84
Syria 63 89
Tajikistan 99
100
Tunisia 83
Turkey 78 94
Uzbekistan
Yemen 29
Make two separate stem plots (one for males and one for females)
What can we say about the shape, outliers, center, and spread of our data?

17. Stem Plots Males Females 2 2 9 3 0 3 18 4 4 6 5 0 5 6 88 6 033 7 0
3 0 4
5 0
7 0
Females
2 9
4 6 5 10
Shape – F – Bi, RS M – Uni, RS
Outliers – Females – 29, 31 Males – 50
Center – F – 71 M – 89
Spread – F – 70 M – 50

18. Answer Example
After analyzing the stem plot that displays the literacy rates for females in Islamic countries, we are able to draw multiple conclusions. The shape of the plot shows that the data is bimodal and right skewed, which could lead us to infer that the majority of women in Islamic countries can read. Our data also shows that there are potential outliers, which could be the reason that our plot is bimodal and right skewed. We also know that the center (median) of our data is at 71%, which also supports our previous inference that the majority of women in Islamic countries can read. Our display also indicates that our data is very spread out (range of 70), which could be a reason for our potential outliers at 29% and 31% as well as the shape of our graph.

19. Check Your Understanding
Use the data for question 1.5 in your textbook (p. 48). Create a stem plot with you data and write a paragraph summary to describe the distribution of the data.
Be sure to address shape, outliers, center, and spread.

20. Foreign Born Residents
Need pg. 35 data
Individuals are the states
Variable is % of a state’s residents who are foreign-born
Enter the data on a TI-84 and make a histogram
Interpret the histogram

21. Making the histogram like we want
Data range from 1.2 to 27.2 so we
could use 0 to 30 with class width 5.
Make a frequency table or relative frequency table.
Label and scale your axes and draw the histogram.

22. Using Histograms Wisely
YOUR ASSIGNED GROUP WILL DESCRIBE ONE OF THE FOLLOWING:
Don’t confuse histograms and bar graphs
Don’t use counts or percents as data
Use percents instead of counts on the vertical axis when comparing distributions with different numbers of observations.
Just because a graph looks nice, it’s not necessarily a meaningful display of data.

23. Changing Class Width
Need One Variable Statistical Calculator applet
With this applet you can drag the horizontal axis with your mouse to change the number of classes. It is then easy to see how the choice of classes affects the histogram.
Try making the class width half as wide. Does this help describe the distribution any better?
How can changing class width and # of classes affect the interpretation?

24. Assignment Read pg. 27-42 Do pg. 42
(37, 41, 43, 45, 53, 59, 60, 69-74)