chapter 6 part 1-2
properties of a normal curve
- the curve is symmetrical about a vertical line through the mu
- the curve approaches the horizontal axis but never touches or crosses it
- the inflection (trasition) points between cupping upward and downward occur above the mu+o and mu-o
- the area under the entire curve is 1
- approximately 68% of the data values will lie within 1 standard deviation on each side of the mean
- approximately 95% of the data values will lie within 2 standard deviations on each side of the mean.
- approximately 99.7% (or almost all) of the data values will lie within 3 standard deviations on each side of the mean
finding standard mean and standard deviation
- Work out the Mean (the simple average of the numbers)
- Then for each number: subtract the Mean and square the result
- Then work out the mean of those squared differences.
- Take the square root of that and we are done!
The control chart is a graph used to study how a process changes over time. Data are plotted in time order and they always have a central line for the average, an upper line for the upper control limit and a lower line for the lower control limit.
These indicate how many standard deviations an element is from the mean. A z-score can be calculated from the following formula. z = (X - μ) / σ where z is the z-score, X is the value of the element, μ is the population mean, and σ is the standard deviation.