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AP STATS Chapter 1 Notes
Friday Sept 11
Exploring Data
Individual- objects described by a set of data (what is on the x-axis)
Variable โ characteristic of the individual
Categorical variable- places individuals in groups โ non numerical
Quantitative variable- numerical values, one can average this data
Distributions- what values the variables take
Bar Graph is a graph that represents categorical data. The bars can be in any order and they do not touch.
Dot Plot is a graph that uses dots to show each piece of data
Enrollment in Introductory Courses at Union University
Read pages 4-10 and do problems 1-6 and finish getting to know you activity
Monday Sept 14
Graphs are the first steps in looking at data. It gives a visual of the data. S โ Shape
O- Outliers Data that appears to fall outside of the overall pattern
One way to get equal intervals is to take the range and divide into equal intervals. You choose how many intervals. You should have at least 5.
(One major error on graph, they did not put in a break in data on the x-axis. This needs to be included.)
Show how to use calculator to make a histogram and input data (page 21)
Percentile
The pth percentile of a distribution is the percent of observations that ball below
Relative cumulative frequency graph (ogive)
The graph starts at 0% and ends at 100%.
Look at graphs page 30
Time plots
Time always goes on the x-axis, showing change over time.
Look for patterns and deviations from the pattern
Trend- long term upward or downward movement over time
Seasonal variation- pattern that repeats itself at regular intervals
Homework Read pages 11-27 and work problems 8,9,10,15,16,and 20
Quiz over section 1.1 on Wednesday
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Data MA
Wednesday Sept 16
Quiz over section 1.
Homework start when done with quix
Read pages 27-34 problems 23,24,
Thursday Sept 17
Describing distributions with numbers
Measuring center
Median โ Middle of the data
Mean - average (add everything up and divide)
Using calculator, put data in a list and do one variable statistics.
x = (x bar)
x = (^) I ฮฃ means sum of all
Mean is sensitive to the influence of extremes
The mean is pulled in the direction of the extremes.
Mean is NOT a resistant measure
Median- Put all numbers in order smallest to largest
Find the middle number. If between two numbers, then average the two numbers to find the median.
Median is resistant to extremes
A box and whisker plot allows us to see how each 25% of the data is distributive. We are normally concerned with the middle 50%.
Inter quartile range (IQR)
IQR = Q 3 โ Q 1
Test for outliers
1.5(IQR) First find this value
Then Q 1 โ (1.5IQR) โ if any data points are lower than this number, they are outliers
Q 3 + (1.5IQR) โ if any data points are higher than this number, they are outliers
Modified box plot โ same as a box plot, except outliers are noted as points instead of part of the whisker
Show how to use calculator.
Show how to do double box plot
Homework Read pages 37-46 problems 31,34,36,
Friday Sept 18
Measuring spread
Standard deviation
How far observations fall from the mean
Smaller standard deviation, data is clustered close to center
Larger standard deviation, data is more spread out
VARIANCE- S^2 Average of the squares of the distance it is from the mean
NEED TO KNOW
******Standard deviation is *********
Standard deviation
You will never do this by hand. It is done with the calculator using a list of data and one variable statistics!!!
Monday September 21
Changing unit of measurement
Linear transformations
Changing units- original variable x
New variable xnew
Xnew = a + bx
a = constant- moves (shifts) whole graph left or right
b โ multiply by a positive constant changes the size of the measurement (affects โ)
Look at problem page 53 โ 54
Put data in calculator page 55
List 1 data list 2 multiply L1 by 110% (1.1)
Find mean and standard deviation for both lists. (use one variable statistics)
List 3 put L1 + 200,000 or L! +.
Find mean and standard deviation
What is the original mean and standard deviation, then L2, then L
What happens, how affected?
Adding a constant to each observation does not change the spread (range or standard deviation)
Linear transformations โ do not change the shape of the distribution
Multiply by b โ mean/median x b, spread and standard deviation or IQR x b
Adding by a โ mean/median add a, spread and standard deviation stays the same
Homework read pages 53-55 do problems 44-
Tuesday September 22
Comparing distributions
Classwork on comparing graphs and matching histograms and box plots
Homework read pages 56-61 problems 48,
Wednesday September 23
Decisions through data
Class work answer al questions and then read pages 64-66 and do problems 60,63,66,
Hand out AP Set for chapter 1
