Chapter 7 lecture notes

Chapter 7 Summarizing and Displaying Measurement Data
Lecture Summary
GOALS FOR CHAPTER 7

1. To illustrate that summarizing important features of a list of numbers provides more information than looking at an unordered list.

2. To explain the concept of the shape of a set of numbers and the vocabulary used to describe shapes, and why it is useful to know something about the shape.

3. To learn the details of how to construct stem-and-leaf plot, histograms and boxplots and how to compute various numerical measures.

4. To discuss what kinds of summaries are best for various kinds of measurements.

Section 7.1 Turning Data into Information
Four kinds of useful information about a set of data: center, variability, shape and outlier
Types of center: mean, median and mode (and their definitions)
Types of variability: range, standard deviation and IQR (and their definitions)
Types of shape: symmetric, skew to the left, skew to the right, unimodal and bimodal (and their definitions)
Definition of outlier (unusual values):
Section 7.2 Picturing Data
Stem-and-leaf plot and how to make a stem-and-leaf plot
Step 1: Create stems
Step 2: Attach leaves
Step 3: Order the leaves
Histogram

Step 1: Divide range of data into intervals.

Step 2: Count how many values fall into each interval. (Create a frequency table)

Step 3: Draw bar over each interval with height = count (or proportion).

Section 7.3 Five Useful Numbers: A Summary
The five number summary (and how to find them)

Definition of IQR (interquartile range)

Section 7.4 Boxplot

How to make a boxplot:

1. Draw horizontal (or vertical) line, label it with values from lowest to highest in data.
2. Draw rectangle (box) with ends at quartiles.
3. Draw line in box at value of median.
4. Compute IQR = distance between quartiles.
5. Compute 1.5(IQR); outlier is any value more than this distance from closest quartile.
6. Draw line (whisker) from each end of box extending to farthest data value that is not an outlier. (If no outlier, then to min and max.)
7. Draw asterisks to indicate the outliers.

Section 7.5 Traditional Measures: Mean, Variance and Standard Deviation

How to calculate for standard deviation:

1. Find the mean.
2. Find the deviation of each value from the mean. Deviation = value – mean.
3. Square the deviations.
4. Sum the squared deviations.
5. Divide the sum by (the number of values) – 1, resulting in the variance.
6. Take the square root of the variance.
The result is the standard deviation.
Formulas for calculating the mean and standard deviation: Mean:

Standard Deviation: