Common Core · High school
HSS-ID.A.4
High school — Use the mean and standard deviation of a data set to fit it to a normal distribution and estimate population percentages.
High school — Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages; recognise that there are data sets for which such a procedure is not appropriate; use calculators, spreadsheets and tables to estimate areas under the normal curve.
The 2 skills that cover it
- Standard Deviation & z-scoresMeasure spread with the average squared distance from the mean, and use z-scores to compare values from different data sets.Read the lesson →
- The Normal DistributionUse the bell curve to turn a value into a proportion and back: the empirical rule, z-scores with a table, percentiles, the value behind a percentage, and comparing scores from different distributions.Read the lesson →
What a student should be able to do
- Compute the variance of a small data set from its mean.
- Compute the standard deviation and state it in the units of the data.
- Convert a value to a z-score and read a z-score back into a value.
- Apply the 68-95-99.7 rule to a roughly bell-shaped data set.
- Use the empirical rule to find the proportion of a normal distribution within or beyond 1, 2 or 3 standard deviations.
- Convert a value to a z-score and use a table to find the proportion below, above or between values.
- Find the value that sits at a given percentile.
- Compare two values from different normal distributions using z-scores.