Math Elementary Statistics and Probability Review Chapter Chapter 1

Transcription

1 Math Elementary Statistics and Probability Review Chapter Chapter 1

2 Math Elementary Statistics and Probability Review Chapter Chapter 1 Review 1. What s statistics The term of statistics is commonly used in two senses. In the first sense, we use the term statistics in our day-to-day communication when we refer to collections of numbers or facts. In the second sense, we define statistics as a scientific subject that provides the techniques of collecting, organizing, summarizing analyzing, and interpreting information in order to draw conclusions (as input to make appropriate decisions). 2. the process of Statistics (4 processes in the consecutive order) (1) Identify the research objective. Collect the information needed to answer the questions posed in (1). Organize and summarize the information(descriptive

3 Math Elementary Statistics and Probability Review Chapter statistics) Draw conclusions from the information(inferential Statistics). 3. Distinguish qualitative(or categorical) variables and quantitative variables 4. what s the difference between variables and data,what s t he difference between continuous variable( or data) and discrete variable(or data) 5. Population. A population is a collection of all conceivable individuals, elements, numbers or entities which possess a characteristic of interest. A portion of a population selected for study is called a sample. The population from which a sample is selected is called a sampled population and the population being studied is called the target population. Every effort is made to ensure the sampled population is the

4 Math Elementary Statistics and Probability Review Chapter same as the target population. Conclusions about the population are valid only if the sample selected is a representative sample, that is, the sample possesses all characteristics of the population that is under investigation.(the techniques of Random Sample) 6. what s the difference between population and sample 7. what s simple random sampling, how to obtain a simple random sample

5 Math Elementary Statistics and Probability Review Chapter Chapter 2

6 Math Elementary Statistics and Probability Review Chapter Chapter 2 Organizing and summarizing data Understand that we take different approaches to organize and summarize the data for different types of variables. I Qualitative Data know how to construct frequency and relative frequency distribution table from your qualitative data(i.e., the raw data). Construct bar graphs/pareto charts/side-by-side bar graphs Pie chart II Quantitative Data know how to construct frequency and relative frequency distribution table from your quantitative data(i.e., the raw data).

7 Math Elementary Statistics and Probability Review Chapter Construct Histograms for discrete or continuous data How to organize continuous data into a frequency and relative frequency table Construct Stem-and-Leaf Plot Time series plots of time series data.

8 Math Elementary Statistics and Probability Review Chapter Statistical Data Qualitative Quantitative Nominal Ordinal interval Ratio

9 Math Elementary Statistics and Probability Review Chapter Statistical Data Qualitative Quantitative Nominal Ordinal interval Ratio

10 Math Elementary Statistics and Probability Review Chapter Misleading Graphs

11 Math Elementary Statistics and Probability Review Chapter Chapter 3

12 Math Elementary Statistics and Probability Review Chapter Chapter 3 Numerically Summarizing Data What s the difference between a parameter and a statistic. 1. A Parameter is a descriptive measure of a population. 2. A statistic is a descriptive measure of a sample. mean mathematical expectation : average : arithmetic average : Example: a sample of size 2: 4 with probability 1/4 and 8 with probability of 3/4 average: 1/2 (4 + 8) = 6 mean: = 7. if all individuals have the same probability (or you assume so), then mean is the same as average. Strictly speaking, mean is a statistical language, but average is more colloquial.

13 Math Elementary Statistics and Probability Review Chapter We have lot of different means arithmetic mean, geometric mean,weighted mean the arithmetic Mean from grouped data(f i s are from the frequency distribution) First calculate the class midpoint Lower class Limit+Upper Class Limit Class midpoint = 2. and then µ = xi f i fi = x 1f 1 + x n f n f 1 + f n f i : the frequency of the ith class. x i : the midpoint of the ith class. n: the number of classes 2. Weighted Mean

14 Math Elementary Statistics and Probability Review Chapter Measure of central tendency and dispersion I Central Tendency 1. distinguish between parameter and statistic 2. the approaches to measure the central tendency(of a population or a sample) and the circumstance to use them arithmetic mean median Mode 3. the approaches to measure the dispersion of a population or sample. Range Variance(or Standard Deviations) 4. the approaches to measure the central tendency of grouped

15 Math Elementary Statistics and Probability Review Chapter data 5. the approaches to measure the dispersion of grouped data 6. the approaches to measure the central tendency of weighted data 7. the approaches to measure the dispersion of weighted data

16 Math Elementary Statistics and Probability Review Chapter Measure the position(or location )- How to describe the relative position of a certain data value within the entire data set. 1. How to measure the location of a observation in a data set Z-score percentiles: How to determine the k-th percentile How to find the percentile for a given data value How to find the quartile os a data set How to check outliers

17 Math Elementary Statistics and Probability Review Chapter the Empirical Rule What s the 68% interval What s the 95% interval What s the 99.7% interval

18 Math Elementary Statistics and Probability Review Chapter The Shape of A Distribution If the Histogram, or Bar graph, or Box-plot, you need to recognize the shape of the distribution Give the relationship between the arithmetic mean and the median of a data set, recognize the shape of the distribution

19 Math Elementary Statistics and Probability Review Chapter Five-Number Summary