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