Review for Exam #1. Chapter 1. The Nature of Data. Definitions. Population. Sample. Quantitative data. Qualitative (attribute) data

Transcription

1 Review for Exam #1 1 Chapter 1 Population the complete collection of elements (scores, people, measurements, etc.) to be studied Sample a subcollection of elements drawn from a population 11 The Nature of Data Quantitative data Definitions numbers representing counts or measurements Qualitative (attribute) data nonnumeric data that can be separated into different categories (categorical data) 3

2 Definitions Discrete - Countable Continuous - Measurements with no gaps Levels of Measurement Nominal - names only Ordinal - names with some order Interval - differences but no zero Ratio - differences and a zero Critical Thinking Voluntary Response Samples Small Samples Graphs Pictographs Percentages Loaded Questions Order of Questions Refusals Etc. 6

3 Methods of Sampling Random Systematic Convenience Stratified Cluster 7 Chapter 33 8 Determine the Definition Values for this Table Quiz Scores Classes Lower Class Limits Upper Class Limits Class Boundaries Class Midpoints Class Width 9

4 Tables Regular Freq. Table Axial Load Relative Freq. Table Axial Load Relative Cumulative Freq. Table Axial Load Cumulative Less than 10 Less than 0 Less than 30 Less than 0 Less than 0 Less than 60 Less than 70 Less than 80 Less than 90 Less than Histogram of Axial Load Data Axial Load (pounds) 11 Important Distributions Normal Uniform Skewed Right Skewed Left 1

5 Stem-Leaf Plots Stem Leaves Mean Measures of Center Median Mode Midrange 1 Calculator Basics for Statistical Data 1. Put calculator into statistical mode. Clear previous data 3. Enter data (and frequency). Select key(s) that calculate x 1

6 Mean for a Table Quiz Scores Midpoints x = 1. ( rounded to one more decimal place than data ) Measure of Variation highest score Range lowest score Measure of Variation Standard Deviation a measure of variation of the scores about the mean (average deviation from the mean) 18

7 Measure of Variation Variance standard deviation squared 19 Same Means (x = ) Different Standard Deviations s = 0 s = 0.8 s = 1.0 s = Standard Deviation 0 Estimation of Standard Deviation Range Rule of Thumb x - s x x + s (minimum usual value) Range s (maximum usual value) Range s = highest value - lowest value 1

8 FIGURE -13 The Empirical Rule (applies to bell-shaped distributions) 99.7% of data are within 3 standard deviations of the mean 9% within standard deviations 68% within 1 standard deviation 3% 3%.%.% 0.1% 0.1% 13.% 13.% x - 3s x - s x - 1s x x + 1s x + s x + 3s Measures of Position z score Sample z = x - x s Population z = x - µ σ 88 Round to decimal places 3 FIGURE -1 Interpreting Z Scores Unusual Values Ordinary Values Unusual Values Z

9 Other Measures of Position Quartiles and Percentiles Finding the Percentile of a Given Score number of scores less than x Percentile of score x = 100 total number of scores percentile of 0 = 100 = is the 18th percentile 6 Start Sort the data. (Arrange the data in order of lowest to highest.) Compute L = ( k ) n where 100 n = number of values k = percentile in question Is L a whole number? No Change L by rounding it up to the next larger whole number. Yes Finding the Value of the kth Percentile Find the 7th percentile. (7 ) 11 = 8.7 = L 100 L = 9 The value of the kth percentile is midway between the Lth value and the next value in the sorted set of data. Find P k by adding the L th value and the next value and dividing the total by. Figure -1 The value of P k is the The 7th percentile is the 9th score, or 1. Lth value, counting from the lowest 7

10 Quartiles Q 1 = P Q = P 0 Q 3 = P 7 8 Boxplot pulse rates (beats per minute) of smokers number summary Minimum - first quartile Q1-60 Median third quartile Q3-78 Maximum Boxplot Box-and-Whisker Diagram Boxplot of Pulse Rates (Beats per minute) of Smokers 30

11 Figure -17 Boxplot Bell-Shaped Uniform Skewed