What’s with all those numbers?
What are Statistics?
1.State the goal of your study precisely. 2.Choose a representative sample from the population. 3.Collect raw data from the sample and summarize. 4.Use the sample statistics to make inferences about the population. 5.Draw conclusions. Collecting Data
A representative sample is a sample in which the relevant characteristics of the sample members match those of the desired population. Samples
1.Simple Random Sampling 2.Systematic Sampling 3.Convenience Sampling Sample Types
To find a mean, you sum all the data and divide by the total number of values. To find a median, you list all the data in order of smallest to largest (or largest to smallest) and choose the middle value. If the data set has an even number of values, find the average of the two middle values. The mode is the value that occurs most often in a data set. Mean, Median, Mode
On a certain exam, students earned the following scores: 98, 96, 96, 93, 87, 84, 76, 67, 67, 67, 62, 51, and 17. Find the mean, median and mode. Mean – Add all the values and divide by 13, the total number of values. Answer = ? Example
On a certain exam, students earned the following scores: 98, 96, 96, 93, 87, 84, 76, 67, 67, 67, 62, 51, and 17. Find the mean, median and mode. Median – Since this data set has an odd number of values, take the number that is in the middle. Example
On a certain exam, students earned the following scores: 98, 96, 96, 93, 87, 84, 76, 67, 67, 67, 62, 51, and 17. Find the mean, median and mode. Mode – Which number occurs most often? Example
The range of a data set is the difference between the largest and smallest values in the data set. Example: On a certain exam, students earned the following scores: 98, 96, 96, 93, 87, 84, 76, 67, 67, 67, 62, 51, and 17. Range : 98 – 17= 81 Range
Standard Deviation
On a certain exam, students earned the following scores: 98, 96, 96, 93, 87, 84, 76, 67, 67, 67, 62, 51, and 17. Find the standard deviation. 1.Find the mean μ. 2.Construct a table as follows. Example
Data PointDifference from μ = 73.9Difference squared 9898 – 73.9 = 24.1(24.1)² = – 73.9 = 22.1(22.1)² = – 73.9 = 22.1(22.1)² = – 73.9 = 19.1(19.1)² = – 73.9 = 13.1(13.1)² = – 73.9 = 10.1(10.1)² = – 73.9 = 2.1(2.1)² = – 73.9 = -6.9(-6.9)² = – 73.9 = -6.9(-6.9)² = – 73.9 = -6.9(-6.9)² = – 73.9 = -11.9(-11.9)² = – 73.9 = -22.9(-22.9)² = – 73.9 = -56.9(-56.9)² = Sum:
Quartiles divide the data into quarters. You will have The low value. The lower quartile, the median of the lower half of data. The median. The upper quartile, the median of the upper half of data. The high value. Quartiles and the 5- Number Summary
On a certain exam, students earned the following scores: 98, 96, 96, 93, 87, 84, 76, 67, 67, 67, 62, 51, and 17. Find the five number summary. Example Low17 Lower Quartile67 Median76 Upper Quartile93 High98
Box plots are a visual representation of the five number summary. Make a vertical mark for each of the five values. Connect the middle three with the use of a box. The high and low are connect to the box by a line. Box Plots
Normal distributions turn up in many of the things we measure about humans. Normal Distributions
Z-Scores
Example