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  1. Lesson 1.1 Day #2 Histograms, Ogives, and Timeplots!

  2. Displaying Quantitative Variables: Histograms Histograms Quantitative lose individual values Making and interpreting stemplots can be tedious for large data sets. For larger amounts of data, ___________ are the most common way to display the distribution of a ___________variable. The disadvantage of a histogram is that you ___________________.

  3. Histograms

  4. Tips: • Divide data into classes of equal width such that each data point falls into only one class. • There is no single correct choice for the number of classes. FIVE is usually a good minimum. • Prepare a frequency table by counting the number of observations in each class.

  5. Tips: 0 • Number and Label your axes and Title your graph. • Draw a bar to represent the count in each class. Remember, NO SPACES between bars (unless the count for that class is ___).

  6. Histograms How Many Children? Frequency 1 3 5 2 4 6 # of children in family How many children are in your family?

  7. Histograms Height of Statistics AP Class Frequency 60 70 80 65 75 Height in inches How tall are you in inches?

  8. Histograms Height of Statistics AP Class Frequency 66 x 71 x 56 x 76 x 61 x Height in inches How tall are you in inches?

  9. ALWAYS Discuss what you see: • Shape – Unimodal? Bimodal? Symmetric? Skewed? What Direction? • Center – estimate the median…about where would you find the middle value? • Spread – What is the range? • Outliers – Do any values seem too far outside the expected range?

  10. Shape! UNIMODAL When you describe the shape of a distribution, concentrate on the main features. Distributions with a single peak (___________) can be described as Symmetric – Skewed right – Skewed left –

  11. Shape! BIMODAL UNIFORM Of course, not all distributions will be unimodal. A distribution could have two peaks (__________), or show no real peaks (___________).

  12. On your Calculator Histograms can be made using the STAT PLOT feature on your calculator (see p. 59). Be sure to set your own WINDOW - Do not ONLYuse the ZOOM STAT feature of your calculator!

  13. Practice Make a histogram of the salary data in your calculator. BE SURE TO SET THE WINDOW APPROPRIATELY! Draw the histogram in your notes.

  14. Chemical Engineering $65,700 Electrical Engineering $60,200 Computer Science $56,400 Economics $50,200 Statistics $48,600 Environmental Science $43,300 Business Administration $43,300 Political Science $41,300 • From www.payscale.com/best-colleges/degrees.asp • July, 2009 Philosophy $40,000 Biology $40,000 Communications $38,700 Fashion Design $36,700 Journalism $36,300 Education $36,200 Graphic Design $36,000 Psychology $36,000 Social Work $33,400 Example: The data* below shows the median starting salary of college graduates with Bachelors Degrees in various fields. Create an appropriate graphical display and describe what you see.

  15. One more thing about histograms • Frequency histogram Relativefrequency histogram Frequency Relative Frequency # of children in family # of children in family

  16. Relative Cumulative Frequency Plots (Ogives) A histogram does not always tell us everything we want to know about a distribution. Sometimes we want to describe the relative position of an individual within a distribution. For this we use a relative cumulative frequency plot (Ogive). The pth percentileof a distribution is the value such that p percent of the observations fall at or below it.

  17. Suppose we want to know the percentile of Statistics majors. In other words, we want to know what percent of majors make the same or less money than Stats majors. Start with the frequency table and add two columns, Cumulative Frequency and Relative Cumulative Freq:

  18. Now, construct a plot with the x-coordinates being the upper end of each class and the y-coordinates being the cumulative frequency.

  19. Ogives a) In what percentile is a Statistician’s salary? b) Find the center of the distribution. What degree earns a salary closest to the center?

  20. Time Plots Time Plots show how a variable changes with time. The time scale goes on the horizontal axis. The variable of interest goes on the vertical axis. Look for trends (long-term upward or downward movement) and seasonal variations.

  21. Time Plots Look for trends (long-term upward or downward movement) and seasonal variations.

  22. Time Plots Look for trends (long-term upward or downward movement) and seasonal variations.