Exploring Data One-Variable (NOTES)

how do you illustrate categorical variable?

bar graph or pie chart

how do you illustrate quantitative varaible?

dot plot

what does frequency table show?

counts (of data collected)

what does relative frequency table show?

proportion (of data collected e.g. 7/10)

what does two-way table show?

summarizes data on the relationship between two categorical variables

what does marginal relative frequency refer to?

the percent or proportion of individuals that have a specific value for one categorical variable— only ONE of the variables in a two-way

what does joint relative frequency refer to?

Gives the percent of proportion of individuals that have a specific value for one categorical variable and a specific value for another categorical variable— BOTH variables in a two-way ("and")

what does conditional relative frequency refer to?

gives the percent or proportion of individuals that have a specific value or one categorical variable among individuals who share the same value of another categorical variable

Do we use frequencies or relative frequencies when comparing data?

relative frequencies

When analyzing numerical categorical data, what phrase do we use?

"A greater percentage of..."

phrases to use when comparing 2 distributions

"greater than" "less than" or "about the same as"

Does association equal causation?

no

How do you describe the distribution of a quantitative variable?

use SOCS (shape, outliers, center, spread/range)

Median equation

(n+1)/2

discrete data

takes certain values— counted (whole numbers)

continuous data

can take any values— measured

mean equation

x̄ = ∑xi/n

SD equation

√[∑(xi-x-bar)^2/n-1]

how does the data (mean, median, mode, range) transform when values are added or subtracted?

only the mean and median changes

how does the data (mean, median, mode, range) transform when values are multiplied or divided?

all of the data (mean, median, mode, range) changes

Components of the 5 number summary

Minimum, Q1, Median, Q3, Maximum

IQR equation

Q3-Q1

equation to find lower outliers

Q1 - 1.5(IQR)

equation to find upper outliers

Q3 + 1.5(IQR)

what does a percentile show?

the percent of values in a distribution that are less than the individual's data value (75th percentile: 75% are below the mean)

percentile equation

(n-1)/total

what does a cumulative frequency graph show?

a point corresponding to the cumulative frequency in each interval at the smallest value of the next interval

what does a z-score show?

how many SD from the mean an observation falls (pos. = above; neg = below)

z-score equation

x-µ/SD

Any score beyond what SD is considered unusual?

2 SDs

mean & SD of normal distributions

Mean= 0

SD= 1

Where do both the median and mean lie at the curve?

the center

If the mean is less than the median, how is the data affected?

It is skewed left

If the mean is greater than the median, how is the data affected?

It is skewed right

How is the curve of a normal distribution split?

68-95-99.7