4E

Skill or Concept: I can . . . Questions to check your understanding Rating
from 1 to 5
Convert values into standardized scores. 1–4
Use a value’s standardized score to determine whether the value is above, below, or equal to the mean. 4
Explain the Empirical Rule. 5

Two people in a room with a doctor who is writing something on a clipboard. Everyone is wearing face masks. A bar graph with the highest bars in the middle and lower bars to either side. In the center, the x-axis is labeled "mu." Three bars to the left, it is labeled "mu - sigma," three more bars to the left it is labeled "mu - 2 sigma," and three more to the left, it's labeled "mu - 3 sigma." Three to the right of the center, it is labeled "mu + sigma." Three more to the right and it is labeled "mu + 2 sigma" and three more to the right, it is labeled "mu + 3 sigma." The center six bars are all green and labeled as 68& collectively. The three leftmost center bars are labeled 34.1%, and the three rightmost center bars are also labeled 34.1%. The next three bars out on either side of the center six are each labeled 13.6% and the center 12 are all labeled 95% collectively. Lastly, the next three out on either side of the center twelve are each labeled 2.1% and all 18 are collectively labeled 99.7% ≈ 100%

Glossary

standardized value
the number of standard deviations an observation is away from the mean. Also referred to as a z-score.
Empirical Rule
a guideline that predicts the percentage of observations within a certain number of standard deviations. Also known as the 68-95-99.7 Rule which states that in a bell-shaped, unimodal distribution, almost all of the observed data values, x, lie within three standard deviations, σ, to either side of the mean, μ. More specifically, about 68% of observations in a dataset will be within one standard deviation of the mean (μ±σ), about 95% of the observations in a dataset will be within two standard deviations of the mean (μ±2σ), and about 99.7% of the observations in a dataset will be within three standard deviations of the mean (μ±3σ).