Warm-up The number of deaths among persons aged 15 to 24 years in the United States in 1997 due to the seven leading causes of death for this age group were accidents, 12,958; homicide, 5,793; suicide, 4,146; cancer, 1,583; heart disease, 1,013; congenital defects, 383; AIDS, 276. Make a bar graph to display these data. What additional information do you need to make a pie chart?
CHAPTER 1 – DAY 2 Histograms
One-Variable Quantitative Data What types of graphs have we looked at so far for quantitative data? The most common graph is a histogram. It is useful for large data sets. NOTE—histograms are appropriate graphs for one-variable quantitative data!!!
Note that the axes are labeled! The bars have equal width!!! The height of each bar tells how many students fall into that class. Bars include the starting value but not the ending value.
Reading a Histogram There are 3 trees with heights between 60 and 64. How many trees have heights between 70 and 79? From 70 to 80? Each value on the scale of the histogram is the START of the next bar.
Let’s practice drawing histograms Follow along on your instruction sheet.
Using the TI Calculator to Construct Histograms Follow the instructions on p. 38 to construct a histogram. Enter the data from p. 39. Note: Clear Y= screen before beginning.
Using Your Calculator Effectively Know that the Xscl sets the width of each histogram bar. XMin and XMax should be a little smaller and a little bigger than the extremes in your data set. Beware of letting the calculator choose the bar width for you.
How to interpret graphs Remember SOCS: Spread, outliers, center, shape Spread—stating the smallest and largest values (note: different from the range where you actually subtract the values). We will talk about other measures of spread later. Outliers—values that differ from the overall pattern. Center—the value that separates the observations so that about half take larger values and about half take smaller values (in the past, you may have heard this called median). Shape—symmetric, skewed left, skewed right, bimodal. We’ll learn more about shape later.
Shape approximately Symmetric – the right and left sides of the histogram are approximately mirror images of each other Skewed Left – there is a long tail to the left Skewed Right – there is a long tail to the right Bimodal – Has two “modes”
Examples of Shape Skewed left!
Skewed right!
Bimodal!
Now what? Constructing the graph is a “minor” step. The most important skill is being able to interpret the histogram. Remember SOCS? Spread Outliers Center Shape
SOCS Spread: from 7 to 22 Outliers: there do not appear to be any outliers. Center: around 15 or 16 Shape: skewed left
One more thing Discuss questions three and four with your group members from page 41.
2005 AP Statistics Problem #1 It’s Never Too Soon for a Practice AP Question
Question 1 Part a) Part a) is graded Essentially Correct, Partially Correct, or Incorrect To receive an Essentially Correct, a student must successfully compare center, shape and spread. Specific numeric values are not required. To receive a Partially Correct, a student must successfully compare 2 of the 3 measures of center, shape and spread. All other responses are graded as Incorrect.
Special Notes Compare means you state which is larger. For example, “the mean of the rural students’ daily caloric intake is greater than the mean for the urban students” is a correct comparison. However, stating “the mean of the rural students’ daily caloric intake is while the mean for the urban students is 32.6” is not a COMPARISON.
In Conclusion Graders were looking for three comparisons: Center—the mean caloric intake of the rural students is greater than the mean caloric intake of the urban students Spread—the spread of the rural students’ distribution is larger than the spread of the urban students Shape—the rural students’ caloric intakes are roughly symmetric while the urban students’ caloric intakes are skewed right.
p. 46 (55, 60, 67, 68, 72, 73, 74) Homework