1. Statistics Chapter 9

2. Statistics Statistics, the collection, tabulation, analysis, interpretation, and presentation of numerical data, provide a viable method of supporting or clarifying a topic under discussion.

3. Statistics Statistical information should illuminate the user’s understanding of the issue or problem at hand.

4. Statistics A population is a collection of all possible elements, values, or items associated with a situation. –A population can contain a finite number of things or it may be nearly infinite. Limitations may be placed on a collection of items to define the population.

5. Statistics A sample is a subset of elements or measurements taken from a population.

6. Statistics Descriptive or deductive statistics describe a population or complete group of data. When describing a population using deductive statistics, the investigator must study each entity within the population. This provides a great deal of information about the population, product, or process, but gathering the information is time-consuming. Inductive statistics deal with a limited amount of data or a representative sample of the population.

7. Statistics Measurement error is considered to be the difference between a value measured and the true value. The error that occurs is one either of accuracy or of precision. Accuracy refers to how far from the actual or real value the measurement is. Precision is the ability to repeat a series of measurements and get the same value each time.

8. Statistics A frequency diagram shows the number of times each of the measured values occurred when the data were collected. This diagram can be created either from measurements taken from a process or from data taken from the occurrences of events.

9. Statistics To create a frequency diagram: 1. Collect the data. Record the measurements or counts of the characteristics of interest. 2. Count the number of times each measurement or count occurs. 3. Construct the diagram by placing the counts or measured values on the x axis and the frequency or number of occurrences on the y axis. The x axis must contain each possible measurement value from the lowest to the highest, even if a particular value does not have any corresponding measurements. A bar is drawn on the diagram to depict each of the values and the number of times the value occurred in the data collected. 4. Interpret the frequency diagram. Study the diagrams you create and think about the diagram’s shape, size, and location in terms of the desired target specification.

10. Statistics Histograms –Similar to frequency diagrams. The most notable difference between the two is that on a histogram the data are grouped into cells. Each cell contains a range of values.

11. Statistics To create a histogram: Step 1: Collect the data and construct a tally sheet Step 2: Calculate the range Step 3: Create the cells by determining the cell intervals, midpoints, and boundaries Step 4: Label the axes Step 5: Post the values Step 6: Interpret the histogram

12. Statistics Analysis of Histograms –Shape, spread, and location are the characteristics used to describe a distribution

13. Statistics –Shape: refers to the form that the values of the measurable characteristics take on when plotted or graphed. –Shape is based on the distributions symmetry, skewness, and kurtosis –Spread: the distance between the highest and lowest values –Location: Where is the distribution in relation to the target?

14. Statistics Measures of Central Tendency –Mean –The mean of a series of measurements is determined by adding the values together and then dividing this sum by the total number of values. –Median –The median is the value that divides an ordered series of numbers so that there is an equal number of values on either side of the center, or median, value. –Mode –The mode is the most frequently occurring number in a group of values.

15. Statistics Measures of Dispersion –Range The range is the difference between the highest value in a series of values or sample and the lowest value in that same series. –Standard Deviation The standard deviation shows the dispersion of the data within the distribution.

16. Statistics The Central Limit Theorem –The central limit theorem states that a group of sample averages tends to be normally distributed; as the sample size n increases, this tendency toward normality improves. –The central limit theorem enables conclusions to be drawn from the sample data and applied to a population.

17. Statistics To Find the Area under the Normal Curve: