AP Statistics Unit 1

(1.6) What are the important characteristics to discuss when describing the distribution of quantitative data?

• Shape (Skewed Left/Right, Symettrical, Unimodal, Bimodal, Uniform)

• Center (Mean, Median)

• Variability/Spread (Range, IQR, Standard Deviation)

• Unusual Features (Outliers, Gaps, Clusters)

(1.7) How do we determine if a value in a data set is an outlier?

• Less than 1.5 times the IQR below Q1 or more than 1.5 times the IQR above Q3

• 2 or more standard deviations away from the mean

(1.7) IQR Formula?

Q₃ - Q₁

(1.7) Standard Deviation Formula

(1.7) What measures are non-resistant?

Mean, Standard Deviation, & Range

(1.7) What measures are resistant?

Mean & IQR

(1.8) How does the shape of a graph influence the relative relationship of the mean and median?

• Skewed right distribution, mean > median

• Skewed left distribution, mean < median

• Symetric distribution, mean = median

(1.9) For a Complete Response when comparing distributions of quantitative date, what is required?

• Address the four important characteristics (Shape, center, variability, unusual features)

• Use Comparative Words

• Include Context

(1.10) Define normal distribution

Model for quantitative data that appears often in real life. It is mound shaped (bell curve) and symmetric.

(1.10) Empirical Rule

States that for a normal distribution:

• Approximately 68% of data falls within 1 standard deviation from the mean.

• Approximately 95% falls within 2 standard deviations.

• Approximately 99.7% falls within 3 standard deviations.

In other words, 68-95-99.7

(1.10) How can percentile be used to describe position of a value in a quantitative data set?

Percentile is the percent of data values less than or equal to a given value.

(1.10) Z-Score?

Z-Score tells us the number of standard deviations above or below the mean

(1.10) How can z-score be used to find percent of data values in given interval for normal distribution?

Left: Get from Table A

Right: 1 - Area from Table A

Between: Subtract two areas from Table A