AP Statistics: One Variable Data

Quantitative Data

Measures of values or counts that are expressed as numbers (e.g. how many, how much, or how often)

Discrete Variable

No decimals, only whole numbers. (Countable)

Continuous Variable

Decimals are okay. (Infinite)

SOCV+Context

Shape, Outlier, Center, Variability + Context

Range

Max - Min

Mean

If the shape is symmetric use the mean

Median

If the shape is skewed us the median

Unimodal

Single peak

Bimodal

Two peaks

What is the best display of data for Quantitative Data?

Histogram (because you don’t have to plot every value)

Histograms

Shows general shape

Dot Plots and Stem Plots

Shows individual values

Q₁

The median of the lower half

Q₃

The median of the upper half

What is the 5 Number Summary

Q₁,Q₃,Minimum, Median, and Maximum

Interquartile Range (IQR)

Q₃-Q₁

<Q₁-1.5IQR

Low Outlier

>Q₃+1.5IQR

High Outlier

What is the worst display of data for Quantitive Data?

Bar Charts because they’re not good for Quantitive Data, they’re only good for Categorical Data

Why can’t you calculate the median on a histogram?

Because the data is grouped and not individual

Low Standard Deviation

Deviation indicates that the data is clustered tightly.

High Standard Deviation

Data points indicates that the data is more spread out.

True or False? Dotplots and Stemplots can show symmetry, gaps, clusters, and outliers.

True

True or False? Sets with different distributions shapes can have identical boxplots.

True

True or False? Box plots, dot plots, stem plots, and histograms can show skewness.

True

True or False? In histograms, relative areas, correspond to relative frequencies.

True

True or False? In histograms, frequencies can be determined from relative heights.

False

Right (Positive) Skew

The mean is higher than the median

Left (Negative) Skew

The median is higher than the mean

Symmetrical

Both the mean and median are roughly equal

True or False frequency charts (histogram or table) can be presented as pie charts?

False because they have different purposes and pie charts tend to only show proportion not count.

The formula for locating and finding the median?

n + 1/2

What is the Standard Deviation?

The distance from the mean

True or False the center + range are never intervals only numbers?

True

Why is the IQR considered to be resistant statistics?

Adding a new extreme observation has little effect on it

True or False box-plots only show percentages?

True

Interpret the Standard Deviation

The context typically varies by SD from the mean.

For SOCV when using Center only use what?

Mean or Median not both

For SOCV when using Variable only use what?

Standard Deviation or IQR not both

Median vs Mean

The "median" refers to the middle value in a set of data when arranged in order, while the "mean" is the average value, calculated by adding up all the values and dividing by the total number of values

Categorical Data

Things that are more word based or something like that such as race, sex, age group, and educational level.