1. Bellwork
1. If a distribution is skewed to the right, which of the following is true? a) the mean must be less than the median b) the mean and median must be equal c) the mean must be greater than the median d) the mean is either equal to or less than the median
2. Which of the following statements are true? (Check one)
I. Categorical variables are the same as qualitative variables. II. Categorical variables are the same as quantitative variables. III. Quantitative variables can be continuous variables.
(A) I only (B) II only (C) III only (D) I and II (E) I and III

2. Graphical Displays Comparing Distributions

3. Notes
Population of Interest: Entire collection of individuals or objects about which information is desired
Sample: Subset of the population, selected for the study
Numerical (Quantitative): Observations are numbers
Discrete: Isolated Points, counting numbers ex. price of textbooks
Continuous: Entire Intervals, real numbers ex. actual weight/length
Categorical (Qualitative): Observations are categories

4. Examples
1) The number of statistics students who do their homework each day
2) The area code of U of A student’s cell phone numbers
3) The amount of gas used to fill up a car

5. Dot Plots
Dotplots:
Quantitative Data
Discrete or Continuous

6. Pie Chart
Pie Chart:
Categorical/Qualitative Data

7. Bar Chart Bar Chart: Used for categorical data The bars do not touch
The bars should be the same width

8. Segmented Bar Graph
The table shows the maximum marks scored by grade 6, 7, and 8 students in math. Which of the following is the correct stacked bar graph for the table shown

9. Histogram Histogram: Used for quantitative data Bars often touch
Bars represent a wide range of values
Shape, center, and spread can be seen

10. The scores for a 25-point quiz are listed below arranged from least to greatest.
7, 7, 12, 13, 15, 16, 16, 16, 18, 19, 20, 20, 20, 21, 21, 22, 23, 23
Using intervals of five points, create a histogram for the class.

11. Histogram Solution
7, 7
12, 13
15, 16, 16, 16, 18, 19
20, 20, 20, 21, 21, 22, 23, 23,

12. Mode
Mode: The general shape of the histogram showing how many peaks there are in the data set
Unimodal: One peak
Bimodal: Two peaks
Multimodal: Numerous peaks

13. Skewness Mean is pulled in the direction of the skew
No Skew: Median, mean, and mode are equal

14. Steam and Leaf Stem and Leaf Plot: Small to moderate data points
What to look for: center, shape, spread, unusual features, outliers
Back to back stem and leaf plot

15. Example:
Make a stem-and-leaf plot out of this set of data and analyze the center, shape and spread.
16, 22, 33, 41, 42, 41, 41, 40, 27, and 18

16. Box Plots
Skeletal Box Plot
Parallel Box Plot

17. upper quartile - lower quartile =IQR
Outliers
Interquartile Range:
Mild Outlier:
Q1 - (1.5)(IQR)
Q3 + (1.5)(IQR)
Extreme Outlier:
Q1 - 3(IQR)
Q3 + 3(IQR)
upper quartile - lower quartile =IQR

18. Check for outliers in the set of data and create a box plot
Check for outliers in the set of data and create a box plot. 21, 23, 24, 25, 29, 49, and 33.
Find the IQR. Since there are seven values in the list, the median is the fourth value, so Q2 = 25.
The first half of the list is 21, 23, 24, so Q1 = 23
The second half of the list is 29, 33, 49, so Q3 = 33.
IQR = 33 – 23 = 10.
Mild Outlier: below 8, above 38
Extreme Outlier: below -7, above 63

20. Frequency Frequency: How many times something occurs
Relative Frequency: Ratio of times something occurs
92 people were asked how they got to work: 35 used a car, 42 took public transport, 8 rode a bicycle, 7 walked
The Relative Frequencies (to 2 decimal places) are:
Car: 35/92 = 0.38
Public Transport: 42/92 = 0.46
Bicycle: 8/92 = 0.09
Walking: 7/92 = 0.08