Standard deviation measures: — The spread or variability of data around the mean.Standard deviation σ measures how spread out data is around the mean. Larger σ = more variability.
Variance is related to standard deviation by: — Variance = σ².Variance σ² = (standard deviation)². Standard deviation σ = √(variance).
Data set: {4, 4, 4, 4, 4}. What is the standard deviation? — 0.All values equal the mean (4). All deviations are 0. Variance = 0. σ = 0. No variability!
The first step in computing standard deviation is to find: — The mean.Step 1: calculate the mean (x̄). Then find deviations from the mean for each data point.
Data: {2, 4, 6}. What is the mean? — 4.Mean = (2 + 4 + 6)/3 = 12/3 = 4.
Data: {2, 4, 6}. The deviations from the mean (4) are: — −2, 0, 2.2−4=−2, 4−4=0, 6−4=2. Deviations always sum to 0.
The standard deviation is in the same _____ as the original data values. — Units.Standard deviation shares the same units as the original data (unlike variance, which is in squared units).
A dataset has variance 25. What is the standard deviation? — 5.σ = √variance = √25 = 5.
The normal distribution is described by its: — Mean μ and standard deviation σ.A normal distribution is completely described by two parameters: its mean μ (center) and standard deviation σ (spread).
The shape of the normal distribution is: — Bell-shaped and symmetric.The normal distribution forms a bell-shaped, symmetric curve centered at the mean.
The Empirical Rule (68-95-99.7) states that about 68% of data falls within: — μ ± σ.About 68% of data falls within μ ± σ (one standard deviation from the mean).
About what percent of data falls within μ ± 2σ? — 95%.The Empirical Rule: 95% of data falls within two standard deviations (μ ± 2σ).
About what percent of data falls within μ ± 3σ? — 99.7%.About 99.7% of data falls within μ ± 3σ — almost all the data.
A z-score formula is z = (x − μ)/σ. A z-score of 0 means: — The value equals the mean.z = 0 means x = μ. The value is exactly at the mean.
The correlation coefficient r measures: — The strength and direction of a linear relationship between two variables.r measures both direction (positive or negative) and strength (−1 to 1) of a linear relationship between x and y.
r = 1 indicates: — Perfect positive linear relationship.r = 1 means a perfect positive linear relationship — all points lie exactly on a line with positive slope.
r = −0.85 indicates: — Strong negative linear relationship.|r| = 0.85 > 0.8 indicates a strong relationship. Negative sign means negative direction. Strong negative linear relationship.
r = 0 indicates: — No LINEAR relationship (but may have nonlinear relationship).r = 0 means no LINEAR relationship. The variables could still have a strong nonlinear relationship.
Least-squares regression minimizes: — The sum of squared residuals.The least-squares line minimizes the sum of SQUARED residuals (SSR), giving the best linear fit.
A residual is defined as: — Actual y − predicted ŷ.Residual = actual y − predicted ŷ. Positive residuals mean the actual value is above the line.
Study hours (x) vs. grade (y): ŷ = 4x + 60. A student studying 0 hours is predicted to score: — 60.y-intercept = 60. ŷ when x = 0: ŷ = 4(0) + 60 = 60.
Same equation ŷ = 4x + 60: A student studying 10 hours is predicted to score: — 100.ŷ = 4(10) + 60 = 40 + 60 = 100.