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
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
Methods of Sampling Random Systematic Convenience Stratified Cluster 7 Chapter 33 8 Determine the Definition Values for this Table Quiz Scores 0- -9 10-1 1-19 0-8 11 7 Classes Lower Class Limits Upper Class Limits Class Boundaries Class Midpoints Class Width 9
Tables Regular Freq. Table Axial Load Relative Freq. Table Axial Load Relative Cumulative Freq. Table Axial Load Cumulative 00-09 10-19 0-9 30-39 0-9 0-9 60-69 70-79 80-89 90-99 9 3 1 3 38 1 00-09 10-19 0-9 30-39 0-9 0-9 60-69 70-79 80-89 90-99 0.01 0.017 0.09 0.03 0.03 0.080 0.183 0.97 0.17 0.08- 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 300 9 1 17 1 39 71 13 161 17 10 Histogram of Axial Load Data 60 0 0 30 0 10 0 199. 09. 19. 9. 39. 9. 9. 69. 79. 89. 99. Axial Load (pounds) 11 Important Distributions Normal Uniform Skewed Right Skewed Left 1
Stem-Leaf Plots 10 11 1 3 7 8 38 38 39 39 0 1 6 6 7 8 6 Stem 1 3 6 Leaves 01 378 8899 0166 78 13 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
Mean for a Table Quiz Scores Midpoints x = 1. ( rounded to one more decimal place than data ) 0- -9 10-1 1-19 0-7 1 17 8 11 7 16 Measure of Variation highest score Range lowest score 66 17 Measure of Variation Standard Deviation a measure of variation of the scores about the mean (average deviation from the mean) 18
Measure of Variation Variance standard deviation squared 19 Same Means (x = ) Different Standard Deviations 7 6 3 s = 0 s = 0.8 s = 1.0 s = 3.0 77 1 1 3 6 7 1 3 6 7 1 3 6 7 1 3 6 7 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
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 -3 - -1 0 1 3 Z
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 99 00 01 0 06 06 08 08 09 1 17 18 percentile of 0 = 100 = 18 11 0 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 00 01 0 06 06 08 08 09 1 17 18 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
Quartiles Q 1 = P Q = P 0 Q 3 = P 7 8 Boxplot pulse rates (beats per minute) of smokers 60 60 60 60 63 63 66 67 68 69 71 7 73 7 78 80 8 83 88 90 - number summary Minimum - first quartile Q1-60 Median - 68. third quartile Q3-78 Maximum - 90 10 10 9 Boxplot Box-and-Whisker Diagram 60 68. 78 90 0 60 6 70 7 80 8 90 Boxplot of Pulse Rates (Beats per minute) of Smokers 30
Figure -17 Boxplot Bell-Shaped Uniform Skewed 31 11 11