AP Stats Unit 1: Describing Distributions, Graphs, Outliers, and Transformations

What does SOCS stand for in describing distributions?

Shape, Outliers, Center, Spread

In a distribution, what indicates the direction of skew?

The direction of the tail

How should outliers be represented on boxplots?

As * or dots

What is the formula for calculating the z-score?

$$z = \frac{\text{value} - \text{mean}}{\text{standard deviation}}$$

What does a positive z-score indicate?

The value is above the mean

What is the 1.5 × IQR rule used for?

To identify outliers

What is the formula for calculating the IQR?

IQR = Q3 − Q1

What happens to the mean and median when a constant is added or subtracted?

They shift but the spread remains unchanged

What is the effect of multiplying or dividing by a constant on mean and spread?

Both the center and spread are multiplied or divided

How do you report the center of a distribution?

By reporting the median or mean with units and context

What is the relationship between mean and median in a symmetric distribution?

Mean is approximately equal to median

What does a larger standard deviation indicate about data?

Data is more spread out from the mean

What are the components of a boxplot?

Minimum, Q1, Median, Q3, Maximum

What is a common trap when interpreting bar charts?

Confusing relative frequency (percentages) with counts

How do you convert relative frequency to counts?

Count = relative frequency × sample size

What is the significance of the 2 SD rule?

It identifies outliers in normal distributions as values outside mean ± 2(SD)

What should you compare when analyzing two distributions?

Shape, center (medians), and spread (IQRs)

What does a smaller standard deviation indicate?

Data is clustered near the mean

What is variance in relation to standard deviation?

Variance = (standard deviation)²

What is the purpose of drawing a histogram from a frequency table?

To visualize the distribution of data