AP Statistics Unit 2 Test

What is a percentile?

The percentile of a value is the percentage of observations less than or equal to it in a distribution.

How do you calculate a percentile rank?

Percentile = (Number of values ≤ your value / Total number of values) × 100.

How do you interpret a percentile?

A value in the 80th percentile is higher than 80% of all other observations.

What is a cumulative relative frequency graph?

A graph showing the cumulative percentage of observations at or below each value; used to find percentiles and estimate values.

How do you find a percentile from a cumulative relative frequency graph?

Locate the desired percentile on the y-axis, move horizontally to the curve, then drop down to find the corresponding value on the x-axis.

How do you find an individual value from a percentile using a cumulative graph?

Locate the percentile on the y-axis, trace horizontally to the curve, and read the corresponding value on the x-axis.

What is a standardized score (z-score)?

A measure that tells how many standard deviations a data value is from the mean.

What is the formula for a z-score?

z=x−meanstandard deviationz=standard deviationx−mean​

What does a positive z-score mean?

The value is above the mean.

What does a negative z-score mean?

The value is below the mean.

What happens to a distribution when you add or subtract a constant to every value?

fThe center (mean, median) shifts by that constant, but the shape and spread (range, SD, IQR) stay the same.

What happens when you multiply or divide every value by a constant?

Both the center and spread are multiplied or divided by that constant; the shape remains the same.

What is a density curve?

A smooth curve that models the distribution of a variable; the area under the curve represents the proportion of observations.

What is always true about a density curve’s total area?

The total area under a density curve is exactly 1.

What do the mean and median represent on a density curve?

The mean is the balance point; the median is the point that divides the area in half.

How do mean and median compare in a symmetric distribution?

Mean = Median.

How do mean and median compare in a skewed-right distribution?

Mean > Median.

How do mean and median compare in a skewed-left distribution?

Mean < Median.

What is the empirical rule (68–95–99.7 rule)?

For Normal distributions

How do you find the proportion of data within an interval using the empirical rule?

Use mean ± k(standard deviation) to find the range, then apply the corresponding percentage (68%, 95%, or 99.7%).

What is the z-table (Table A) used for?

To find the area (proportion) under the standard Normal curve to the left of a given z-score.

How do you find the proportion of values between two z-scores?

Find the area to the left of each z-score from the table, then subtract the smaller from the larger.

How do you find a z-score from a given percentile using Table A?

Locate the percentile (area) in the table, then find the z-score corresponding to that cumulative area.

How do you find a data value (x) from a percentile in a Normal distribution?

Use x=μ+(z×σ)x=μ+(z×σ), where z corresponds to the percentile.

How do you determine if data is approximately Normal from a graph?

Look for a symmetric, unimodal shape in a histogram or bell curve.

How can a Normal probability plot help assess normality?

If the points form an approximately straight line, the data is approximately Normal.

What are numerical indicators that data may be Normal?

Mean ≈ median, and the empirical rule closely applies.

When should you not use Normal distribution models?

When the data is strongly skewed or has clear outliers.

What is the relationship between area under a density curve and probability?

The area under the curve in a given interval equals the probability that a randomly chosen value falls in that interval.

What is the standard Normal distribution?

A Normal distribution with mean = 0 and standard deviation = 1.

What is the symbol for the mean in a population?

μ (mu).

What is the symbol for standard deviation in a population?

σ (sigma).

What is the shape of a Normal distribution?

Symmetric, bell-shaped, single-peaked.

How do you convert any Normal variable to a standard Normal variable?

Subtract the mean and divide by the standard deviation (to get z).

How do you check if data follows the empirical rule?

Calculate the % of observations within 1, 2, and 3 SDs of the mean and compare to 68%, 95%, and 99.7%.