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Data Analysis Essentials: Measures of Center and Variation

Learn how to open and analyze data files in Minitab, understand data storage, generate histograms, and calculate numerical measures such as mean, median, quartiles, variance, and standard deviation.

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Data Analysis Essentials: Measures of Center and Variation

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  1. Minitab • How to open a data file? • How is the data stored? • Generate Histogram

  2. Numerical Measures • Center (where is middle?) • Variation (how much does it vary?)

  3. (Sample) Mean (Sample) Median the number in the middle Measures of Center

  4. Example • Birth weight of five babies born in a hospital: 9.2, 6.4, 10.5, 8.1, 7.8 • Mean birth weight = (9.2+6.4+10.5+8.1+7.8)/5= 8.4 • Median 6.4 7.8 8.1 9.2 10.5

  5. Another Example • Survival Time: 3 15 46 64 126 623 • Mean survival time = (3+15+46+64+126+623)/6 = 146.2 days • Median • (46+64)/2 = 55 days

  6. Median less affected by extreme observations (outliers) • Median is more sensible measure for extreme asymmetrical data

  7. Sample 100p-th Percentile • Order the data from the smallest to largest • Determine np • If np is not an integer, round it up, say k, and find the kth ordered value. • If np is an integer, say k, find the average of the kth and the (k+1)th ordered value.

  8. Sample Quartiles • First (Lower) Quartile Q1= 25th percentile • Second Quartile (Median) Q2= 50th percentile • Third (Upper) Quartile Q3= 75th percentile

  9. Traffic Noise Level in Decibels 52.0 54.4 54.5 55.7 55.8 55.9 55.9 56.2 56.4 56.4 56.7 56.8 57.2 57.6 58.9 59.4 59.4 59.5 59.8 60.0 60.2 60.3 60.5 60.6 60.8 61.0 61.4 61.7 61.8 62.0 62.1 62.6 62.7 63.1 63.6 63.8 64.0 64.6 64.8 64.9 65.7 66.2 66.8 67.0 67.1 67.9 68.2 68.9 69.4 77.1

  10. Measures of Variation Two data set: 1 2 3 4 5 2 3 3 3 4

  11. Variance and Standard Deviation • Sample Variance s2 = (sum of squared deviations) /(n-1) • Sample Standard Deviation s = Square Root of Variance

  12. Sample Variance s2 = 10/(5-1)=2.5 • Sample Standard Deviation

  13. 68-95-99.7 rule If the distribution is bell sharp, then approximately • 68% of the data lie with • 95% of the data lie with • 99.7% of the data lie with

  14. Boxplot • Five Number Summary • Minimum • Q1 • Median • Q3 • Maximum • Inter-Quartile Range: Q3-Q1

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