AP Statistics Chapter 1: Exploring Data Preliminary
Statistics: the science of data. Using a small group (sample) to make conclusions about the whole (population).
Where do we get data?
Personal experience – no. times you get a phone call
Available data – government, internet
Collect it
Observational study – observe but don’t influence, survey
Experimental study – do something to observe response
Key points about data:
Who is described by the data (how many)
What are the variables (and their units)
Why is the data gathered
When, where, how, by whom were the data produced.
Variable Types
Categorical variable:
places an individual into one of several groups of categories.
Described by bar graphs
Quantitative variable:
Specific quantity
Use dot plot, stem plot
Distribution:
pattern of variation of a variable
tells what values the variable takes and how often it takes these values.
Homework: p.11 1 – 5 odd p. 19 7, 8, 9, 12
AP Statistics Chapter 1: Exploring Data Section 1.1 Displaying Distribution with Graphs
• Graphs used to display data:
• bar graphs, pie charts, dot plots, stem plots, histograms, and time plots
• Purpose of a graph:
• Helps to understand the data.
• Allows overall patterns and striking deviations from that pattern to be seen.
• Describing the overall pattern:
• Three biggest descriptors:
• shape, center and spread.
Next look for gaps and possible outliers. Outliers- don’t delete or ignore; figure out why they exist
Always include title and labels!!!
Properly number the number line with boxplots!!!!
ALWAYS discuss shape, center, and spread
These are the most common shapes. Label the mode, median, mean on each graph.
Dotplots – Procedure
1. Draw an x and y axis and mark it with an appropriate measurement scale.
2. Locate each value in the data set along the measurement scale, and represent it by a dot. If there are two or more observations with the same value, stack the dots vertically.
To compare the weights of the males and females we put the dot plots on top of each other, using the same scale.
Stemplots - Separate the numbers into leaf (last #) and stem. State a title (with units) and key ( to know how to read it).
Weights of the 25 female students:
150 140 155 195 139
200 157 130 113 130
121 140 140 150 125
135 124 130 150 125
120 103 170 124 160
The following are the GPAs for the 20 advisees of a faculty member.
GPA
3.09 2.04 2.27 3.94 3.70 2.69 3.72 3.23 3.13 3.50 2.26 3.15 2.80 1.75 3.89 3.38 2.74 1.65 2.22 2.66
If the ones digit is used as the stem, you only get three groups. You can expand this a little by breaking up the stems by using each stem twice letting the 2nd digits 0-4 go with the first and the 2nd digits 5-9 with the second.
Comparative Stem and Leaf Diagram Example: student weight (comparing 2 groups). What is missing in this plot?
Histograms - breaks range of values into classes (use = widths)
Like a bar chart, but for quantitative data.
Like a stem ploy/ dot plot, but better for more data
To make a histogram:
1. Divide the range into equal widths. Then count the number of observations that fall in each group. If a number falls on a class then “bump up” into next class.
2. Label and scale your axes and title your graph.
3. Draw bars that represent each count, no space between bars.
P59-60 shows example how to produce on calc
Divide range into equal widths and count
Create the graph. Describe visually
CEO Salary in thousands of dollars
Homework: p. 55 7 – 10, 12
Relative frequency:
Category count divided by the total count
Gives a percentage
Should add up to 100%. Why might it not?
Cumulative frequency:
Sum of category counts up to an including the current category
Ogives (pronounced O-Jive)
Cumulative frequencies divided by the total count
Relative cumulative frequency graph
Be able to read it and create a histogram or box plot from it
Percentile:
The pth percentile of a distribution is the value such that p percent of the observations fall at or below it.
Lets look at a table to see what an ogive would refer to.
The graph of an ogive for this data would look like this.
Find the age of the 10th percentile, the median, and the 85th percentile.
List the age of your parents: make a stem plot, make a histogram, analyze them, then make an ogive.
Age Data
Frequency / Relative Frequency / Cumulative Frequency / Relative Cumulative Frequency30-34
35-39
40-44
45-49
50-54
55-59
60-64
65-69
70-74
Homework: p. 64 13, 14 p. 68 23, 25, 26