Chapter 1: Exploring Data

1. Chapter 1: Exploring Data AP Stats Mr. Warren 2011-2012

2. 1.1 Displaying Distributions With Graphs The table above displays the sales figures and market share achieved by several major soft drink companies in 1999.

3. 1.1 Displaying Distributions With Graphs • How could we display this table graphically?

4. 1.1 Displaying Distributions With Graphs • Steps to a Bar Graph • Step 1: Label your axes and TITLE YOUR GRAPH. • Draw a set of axes. Label the horizontal axis “Company” and the vertical axis “Cases Sold”. • Title your graph • Step 2: Scale your axes. • Use the counts in each category to help you scale your vertical axis . • Write the category names at equally spaced intervals beneath the horizontal axis. • Step 3: Draw a vertical bar above each category name to the appropriate height.

5. 1.1 Displaying Distributions With Graphs • How to Construct a Pie Chart: • Use Technology!

6. 1.1 Displaying Distributions With Graphs • When do we use a bar graph? • To describe quantities of categorical data. • When do we use a pie chart? • To describe percentages of a whole of categorical data

7. 1.1 Displaying Distributions With Graphs

8. 1.1 Displaying Distributions With Graphs

9. 1.1 Displaying Distributions With Graphs • The NPHS Varsity Football team scored the following number of points in their games for the past three years: • 50, 51, 23, 27, 10, 31, 17, 56, 30, 59, 26, 14, 41, 33, 19, 27, 20, 9, 23, 42, 15, 26, 14, 21, 19, 37, 28, 27, 21, 44 • Create three graphical displays of this data: • Dot Plot • Stem Plot • Histogram

10. 1.1 Displaying Distributions With Graphs • Steps to Making a Dot Plot • Step 1 Label your axis and TITLE YOUR GRAPH. • Draw a horizontal line and label it with the variable. • TITLE YOUR GRAPH • Step 2: Scale the axis based on the values of the variable. • Step 3: Mark a dot above the number on the horizontal axis corresponding to each data value.

11. 1.1 Displaying Distributions With Graphs

12. 1.1 Displaying Distributions With Graphs • Describe the Distribution • Shape – the data has a peak at 27 meaning the most frequent score was 27 points, the data is skewed to the right. • Center – The median of the data is approximately 27, could also talk about the mean. • Spread – The data has a low value of 9 and a high value of 59 giving a range of 50. • Outliers – The data appears skewed right but there do not appear to be any outliers.

13. 1.1 Displaying Distributions With Graphs • Shape • Approximately Symmetric – right and left sides are approximately mirror images • Skewed Right – the right side of the distribution is stretched out, most of the data is to the left scared away from the right side • Skewed Left - the left side of the distribution is stretched out, most of the data is to the right scared away from the left side • Bi-Modal – Two points of high frequency, you would list both points of high frequency • Uniform – Data is approximately the same all the way across the distribution • Center • Mean • Median • Spread • Low Value to High Value • Range of • Inner Quartile Range • Standard Deviation • Outliers • Check for Outliers ( Hold tight, eyeball it for now!)

14. 1.1 Displaying Distributions With Graphs • Steps to a Stem Plot • Step 1: Separate each observation into a stem consisting of all but the rightmost digit and a leaf, the final digit. • Step 2: Write the stems vertically in increasing order from top to bottom, and draw a vertical line to the right of the stems. Go through the data writing each leaf to the right of its stem and spacing the leaves equally. • Step 3: Write the stems again, and rearrange the leaves in increasing order out from the stem, • Step 4: TITLE YOUR GRAPH and add a key describing what the stems and leaves represent.

15. 1.1 Displaying Distributions With Graphs • 0 9 • 1 0 4 4 5 7 9 9 9 • 2 0 0 1 1 3 3 6 6 7 7 7 7 8 • 3 0 1 3 7 • 4 1 2 • 5 0 1 6 9 • 5 | 0 = 50 points scored in a game NPHS Football scores for 2008 – 2010

16. 1.1 Displaying Distributions With Graphs • Describe the distribution: • Any time we hear this phrase what do we have to talk about? • 1. • 2. • 3. • 4.

17. 1.1 Displaying Distributions With Graphs • Steps to Making Histograms • Step 1: Divide the range of the data into classes of equal width. Count the number of observations in each class. • Step 2: Label and scale your axes and title your graph. • Step 3 Draw a bar that represents the count in each class. The base of the bar should cover its class, and the bar height is the class count. Make sure the bars touch.

18. Presidential Age at Inauguration

19. 1.1 Displaying Distributions With Graphs • Classes • 40 < president’s age at inauguration < 45 • 45 < president’s age at inauguration < 50 • 50 < president’s age at inauguration < 55 • 55 < president’s age at inauguration < 60 • 60 < president’s age at inauguration < 65 • 65 < president’s age at inauguration < 70

20. 1.1 Displaying Distributions With Graphs

21. 1.1 Displaying Distributions With Graphs • What is wrong with this graph? • What is missing?

22. 1.1 Displaying Distributions With Graphs • Now that we have fixed our histogram: • Describe the distribution: • 1. • 2. • 3. • 4.

23. 1.1 Displaying Distributions With Graphs • Let’s do the histogram with your calculator now!

24. How to construct an OgiveRelative Cumulative frequency graph • Step 1 Decide on class intervals and make a frequency table, just like a histogram. Add three columns to your frequency table: relative frequency, cumulative frequency, and relative cumulative frequency.

25. Relative Cumulative Frequency column is for the ogive

26. How to construct an OgiveRelative Cumulative frequency graph • Step 2: Label and scale your axes then title your graph. Horizontal axes, “Age at Inauguration”. Vertical axis “Relative Cumulative Frequency” • Step 3: Plot a point corresponding to the relative cumulative frequency in each class at the left endpoint of the of the next class interval. See Figure 1.12