Slide 4 7 7 Steamrolled Example Compare the histogram and steamrolled display for the pulse rates of 24 women at a health clinic. Which graphical display do you area principle. Prefer? Slides 8 8 Constructing a Steamrolled Display First, cut each data value into leading digits (“stems”) and trailing digits (“leaves”). Use the stems to label the bins. Use only one digit for each leaf?either round or truncate the data values to one decimal place after the stem. Slide 4 9 9 Topless A topple is a simple display. It just places a dot along an axis for each case in the data. The topple to the right shows Kentucky Derby winning times, plotting each race as its own dot. You might see a topple displayed rationally or vertically. Slide 4 10 10 Think Before You Draw, Again Remember the “Make a picture” rule? Now that we have options for data displays, you need to Think carefully about which type of display to make. Before making a southeastern display, a histogram, or a topple, check the: > Quantitative Data Condition: The data are values of a quantitative variTABLE whose units are known.
Slides 11 11 Shape, Center, and Spread When describing a distribution, make sure to always tell about three things: shape, center, and spread… Slides 12 12 What is the Shape of the Distribution? Does the histogram have a single, central hump or several separated humps? Is the histogram symmetric? Do any unusual features stick out? Slides 13 13 Humps or several separated bumps? > Humps in a histogram are called modes. > A histogram with one main peak is dubbed individual; histograms with two peaks are bimodal; histograms with three or more peaks are called multimode.
Slide 4 14 14 Humps (count. ) A bimodal histogram has two apparent peaks: Slides 15 15 A histogram that doesn’t appear to have any mode and in which all the bars are approximately the same height is called uniform: Slide 4 16 16 August 1 7, 201 3 Symmetry Is the histogram symmetric? If you can fold the histogram along a vertical line through the middle and have the edges match pretty closely, the histogram is symmetric. Slide 4 17 17 Symmetry (count. ) The (usually) thinner ends off distribution are called the tails.
If one tail stretches out farther than the other, the histogram is said to be skewed to the side of the longer tail. In the figure below, the histogram on the left is said to be skewed left, while the histogram on the right is said to be skewed right. Slides 18 18 Anything Unusual? Sometimes it’s the unusual features that tell us meeting interesting or exciting about the data. You should always mention any stragglers, or outliers, that stand off away from the body of the distribution. Are there any gaps in the distribution?
If so, we might have data from more than one group. Slides 19 19 Anything Unusual? (count. ) The following histogram has outliers? three cities in the leftmost bar: Slide 4 20 20 there are Where is the Center of Distribution? If you had to pick a single number to describe all the data what would you pick? It’s easy to find the center when a histogram is individual and symmetric?it’s right in the middle. On the other hand, it’s not so easy to find the center of a skewed histogram or a histogram with more than one mode.
Slide 4 21 21 Center off Distribution Median The median is the value with exactly half the data values below it and half above it. It is the middle data value (once the data values have been ordered) that divides the histogram into two equal areas It has the same units as the data Slide 4 22 22 How Spread Out is the Distribution? Variation matters, and Statistics is about variation. Are the values of the distribution tightly clustered around the center or more spread out? Always report a measure of spread along with a measure of center when describing a distribution numerically.
Slide 4 23 23 Spread: Home on the Range The range of the data is the difference between the maximum and minimum values: – Range = Max- min A disadvantage of the range is that a single extreme value can make it very large and, thus, not representative of the data overall. Slides 24 24 Spread: The Interrelate Range *The interrelate range (SIR) lets us ignore extreme data values and concentrate on the middle of the data. *To find the SIR, we first need to know what quartiles are…