Stat misleading graphs
How to make a stemplot
Create stem, add leaves, order leaves, add a key Ex: Numbers 15, 17, 28, 29 and 42 1|57 2|89 4|2 Key: 4|2 represents a student that has 42 shoes
How to spot a misleading graphic:
1. It may not have axis labels or scale. 2. It may cut off the x or y axis, or start at a weird place. 3. It may use pictures for bar graphs (or a 'pictograph').
Stemplot
Also called a stem-and-leaf plot. Data are separated into a stem and leaf by place value and organized in the form of a histogram.
categorical data
Data that fits an individual into one of several categories that don't have an order. Usually represented by counts or percentages, and isn't a number (but it can be). Ex: eye color, race, gender, social security number, and zip code.
quantitative data
Data that is numerical (think 'quantities'). Usually a measurement. You can line the values up in order. Ex: weight, # of AP classes, SAT score, blood pressure, income, yards per catch, etc.
How to compare multiple distributions of data
Explicitly compare the center and variability of each, using words like "greater than," "less than," or "about the same as."
How to describe the pattern of a graph
Identify shape, center, variability, and outliers (CONTEXT NEEDED FOR EACH)
If skewed to the left, is the mean greater than or less than the median?
Mean < Median
If skewed to the right, is the mean greater than or less than the median?
Mean > Median
What is a resistant measure of the center, median or mean?
Median
What number is also the second quartile?
Median
IQR formula
Q3-Q1
Histogram detriments/benefits
Show shape of quantitative data
Dotplot detriments/benefits
Shows shape of quantitative data
What is standard deviation
Square root of the variance: roughly how far away each number is from the mean
How to describe center
State the median/mean
How to find first and third quartile
Take numbers between the first value and the last number before going over the median, find the median of those numbers
Tip on skewing in graphs:
The direction of skewness is toward the long tail, not the direction where most observations are clustered.
skewed right distribution
The peak of the data is to the left side of the graph. There are only a few data points to the right side of the graph. Tail of graph is on right side.
Skewed Left Distribution
The peak of the data is to the right side of the graph. There are only a few data points to the left side of the graph. Tail of graph is on left side.
spread of a data distribution
a measure of the amount of variability, or how "spread out" a set of data is
mode of a data set
any value that occurs with the greatest frequency
detriments/benefits of stemplots
can't use for big sets of quantitative data good for small sets and comparing quantitative data
How to describe shape
identify any gaps in the graph if skewed or symmetric state the peak in graph
5 number summary of a boxplot
min, max, Q1, Q3, median
Are standard deviation and mean resistant or nonresistant?
nonresistant
What is best to graph categorical data
pie chart/ bar graph
Detriment of boxplot, benefit of boxplot
show less data good for comparing multiple sets of data and their centers
Measure variation
standard deviation, range, and clusters
Equation to determine outliers, bottom quartile
x < Q1 - 1.5(IQR)
does the standard deviation depend on the mean
yes because it is calculated from the mean