Statistics: Week 3

 Week 3: Standard Deviation and Normal Distributions

Day 1:
Labor Day



Day 2:
Standard Deviation - the "average" distance from the mean value. It is called Sx and is equal to the blue stuff on the right.

Day 3:
Matching Summary Stats to Histograms and The Effect of Changing Units Simulation.

You can match the 5-number summary and the Std. Dev. and mean to histograms.

When you change the units of a data set by a scalar multiple, all of that data set's number summaries are also multiplied by that same scalar multiple.

When you add a set number to every value in a data set, out of the number summaries, only the mean and median are also increase by that number.

Day 4:
Density Curves/Normal Distributions

A density curve is a graph of data values where the total area under the curve is equal to 1. You can get a density curve by tracing the approximate heights of a histogram and setting the y-axis scale so that the total area under the curve is equal to 1.

Normal distributions are bell curves. These are symmetrical, bell-shaped density curves. 2 characteristics define a normal distribution: µ, which stands for the mean, and σ, which stands for the standard deviation.

The 68-95-99.7 rule states that 68 percent of values in a normal distribution fall within 1 standard deviation, 95, within 2 standard deviations, and 99.7 within 3.

Day 5:
z-scores, Percentiles and Standard Normal

z-score = (x - µ )/ σ

z-scores tell how many standard deviations a vlaue is from the mean. A graph of z-scores gives you a standard normal curve. This curve is used to determine the percentiles of values that do not fall on whole standard deviations where the 68-95-99.7 rule can be applied.

Tests
This Week Tests: None

Future Tests: Quiz #2 next Tuesday and Test Chapers 1&2 next Friday